9000 Number Patterns Worded Questions

1) On a trout farm, there is a starting population of 800 fish. The fish population increases by 40% every six months. How many fish are on the farm after 3 years?

After 3 years = t7

Explanation

After 3 years = t7

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2) On a trout farm, there is a starting population of 1000 fish. The fish population increases by 50% every six months. How many fish are on the farm after 2 years?

After 6 months, the fish population increases by 50%, so there will be 1000 * 1.5 = 1500 fish.
After another 6 months, the population increases by 50% again, so there will be 1500 * 1.5 = 2250 fish.
After 1 year, the population will be 2250 * 1.5 = 3375 fish.
After 2 years, the population will be 3375 * 1.5 = 5062.5 fish.
Since we can't have half a fish, we round up to the nearest whole number, so the final answer is 5063 fish.

Explanation

After 6 months, the fish population increases by 50%, so there will be 1000 * 1.5 = 1500 fish.
After another 6 months, the population increases by 50% again, so there will be 1500 * 1.5 = 2250 fish.
After 1 year, the population will be 2250 * 1.5 = 3375 fish.
After 2 years, the population will be 3375 * 1.5 = 5062.5 fish.
Since we can't have half a fish, we round up to the nearest whole number, so the final answer is 5063 fish.

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3) At the local lake, there is a starting population of 2000 fish. The fish population is decreased by 10% every month through fisherman catching them. If none are replaced or die, how many fish are on the farm after 1 year?

The fish population decreases by 10% every month due to fishermen catching them. After 1 year, which is 12 months, the population will be reduced by 10% each month for a total decrease of 120%. Therefore, the remaining population will be 100% - 120% = -20%. However, a population cannot be negative, so the correct answer is 0.

Explanation

The fish population decreases by 10% every month due to fishermen catching them. After 1 year, which is 12 months, the population will be reduced by 10% each month for a total decrease of 120%. Therefore, the remaining population will be 100% - 120% = -20%. However, a population cannot be negative, so the correct answer is 0.

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4) On a trout farm, there is a starting population of 700 fish. The fish population increases by 80% every year. How many fish are on the farm after 3 years?

The fish population on the trout farm increases by 80% every year. To find the population after 3 years, we need to calculate the population after each year and then add them up. After the first year, the population increases by 80% of 700, which is 560. So, after the first year, the population is 700 + 560 = 1260. After the second year, the population increases by 80% of 1260, which is 1008. So, after the second year, the population is 1260 + 1008 = 2268. After the third year, the population increases by 80% of 2268, which is 1814.4. So, after the third year, the population is 2268 + 1814.4 = 4082.

Explanation

The fish population on the trout farm increases by 80% every year. To find the population after 3 years, we need to calculate the population after each year and then add them up. After the first year, the population increases by 80% of 700, which is 560. So, after the first year, the population is 700 + 560 = 1260. After the second year, the population increases by 80% of 1260, which is 1008. So, after the second year, the population is 1260 + 1008 = 2268. After the third year, the population increases by 80% of 2268, which is 1814.4. So, after the third year, the population is 2268 + 1814.4 = 4082.

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5) On a trout farm, there is a starting population of 900 fish. The fish population increases by 35% every year. How many fish are on the farm a the start of the 4th year?

The fish population increases by 35% every year, which means that each year the population multiplies by 1.35. To find the population at the start of the 4th year, we need to multiply the starting population of 900 by 1.35 three times (since it is the 4th year).

900 * 1.35 * 1.35 * 1.35 = 2214

Therefore, there are 2214 fish on the farm at the start of the 4th year.

Explanation

The fish population increases by 35% every year, which means that each year the population multiplies by 1.35. To find the population at the start of the 4th year, we need to multiply the starting population of 900 by 1.35 three times (since it is the 4th year).

900 * 1.35 * 1.35 * 1.35 = 2214

Therefore, there are 2214 fish on the farm at the start of the 4th year.

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6) On a trout farm, there is a starting population of 1200 fish. The fish population increases by 20% every year. How many fish are on the farm at the start of the 5th year?

The fish population increases by 20% every year, which means that each year the population will be multiplied by 1.2. To find the population at the start of the 5th year, we need to multiply the starting population of 1200 by 1.2 four times (for each year).

1200 * 1.2 * 1.2 * 1.2 * 1.2 = 2488

Therefore, there will be 2488 fish on the farm at the start of the 5th year.

Explanation

The fish population increases by 20% every year, which means that each year the population will be multiplied by 1.2. To find the population at the start of the 5th year, we need to multiply the starting population of 1200 by 1.2 four times (for each year).

1200 * 1.2 * 1.2 * 1.2 * 1.2 = 2488

Therefore, there will be 2488 fish on the farm at the start of the 5th year.

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7) A water tank has a leak and needs repairs. It currently contains 19000 litres of water. A pump is hooked up to the outlet that drains out 650 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

Since the pump drains out 650 litres per minute, it will take 30 minutes to drain the entire tank of 19000 litres.

Explanation

Since the pump drains out 650 litres per minute, it will take 30 minutes to drain the entire tank of 19000 litres.

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8) A water tank has a leak and needs repairs. It currently contains 18000 litres of water. A pump is hooked up to the outlet that drains out 850 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

Since the pump drains out 850 litres per minute, and the tank currently contains 18000 litres of water, we can calculate the time it takes to empty the tank by dividing the initial amount of water in the tank by the rate at which it is being drained. Therefore, 18000 divided by 850 equals approximately 21.18. Since we cannot have a fraction of a minute, it will take 22 minutes for the tank to be empty.

Explanation

Since the pump drains out 850 litres per minute, and the tank currently contains 18000 litres of water, we can calculate the time it takes to empty the tank by dividing the initial amount of water in the tank by the rate at which it is being drained. Therefore, 18000 divided by 850 equals approximately 21.18. Since we cannot have a fraction of a minute, it will take 22 minutes for the tank to be empty.

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9) You purchase a house for $380,000 as an investment over the long term. However, over the last three years, the area you has had a rise in crime, and the prices have been declining by 8% per annum. How much is your unit worth after three years? (to the nearest thousand dollars)

After three years, the house's value will have declined by 8% each year. To calculate the final value, we can multiply the original value ($380,000) by 0.92 (100% - 8% = 92%).

$380,000 * 0.92 = $349,600

Therefore, the house will be worth $349,600 after three years. However, the answer choices provided are $296,000 and $296,000, which do not match the calculated value. Therefore, the correct answer cannot be determined from the given options.

Explanation

After three years, the house's value will have declined by 8% each year. To calculate the final value, we can multiply the original value ($380,000) by 0.92 (100% - 8% = 92%).

$380,000 * 0.92 = $349,600

Therefore, the house will be worth $349,600 after three years. However, the answer choices provided are $296,000 and $296,000, which do not match the calculated value. Therefore, the correct answer cannot be determined from the given options.

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10) A water tank has a leak and needs repairs. It currently contains 17000 litres of water. A pump is hooked up to the outlet that drains out 650 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

Since the pump drains out 650 litres per minute, it will take 27 minutes to drain out the entire tank of 17,000 litres of water.

Explanation

Since the pump drains out 650 litres per minute, it will take 27 minutes to drain out the entire tank of 17,000 litres of water.

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11) You are offered a job with a company on a starting wage of $25,500 and an annual increment of $800. What is your wage at the start of the 5th year with the company?

The starting wage of $25,500 increases annually by $800. Therefore, after the first year, the wage would be $25,500 + $800 = $26,300. After the second year, it would be $26,300 + $800 = $27,100. After the third year, it would be $27,100 + $800 = $27,900. After the fourth year, it would be $27,900 + $800 = $28,700. Therefore, at the start of the fifth year, the wage would be $28,700.

Explanation

The starting wage of $25,500 increases annually by $800. Therefore, after the first year, the wage would be $25,500 + $800 = $26,300. After the second year, it would be $26,300 + $800 = $27,100. After the third year, it would be $27,100 + $800 = $27,900. After the fourth year, it would be $27,900 + $800 = $28,700. Therefore, at the start of the fifth year, the wage would be $28,700.

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12) I have 60 building blocks. I want to build a tower with 1 block on the top, 2 on the next layer and 3 on the next layer. How many complete layers can I build before I run out of blocks?

You can calculate the number of complete layers by finding the sum of the natural numbers from 1 to n, where n is the number of layers. The formula for the sum of natural numbers is n(n+1)/2. By solving the equation 60 = n(n+1)/2, you find that n is approximately 10. Therefore, you can build 10 complete layers before running out of blocks.

Explanation

You can calculate the number of complete layers by finding the sum of the natural numbers from 1 to n, where n is the number of layers. The formula for the sum of natural numbers is n(n+1)/2. By solving the equation 60 = n(n+1)/2, you find that n is approximately 10. Therefore, you can build 10 complete layers before running out of blocks.

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13) I have 70 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

You can build 8 complete layers before running out of blocks. Each layer requires an odd number of blocks, starting with 1, then 3, 5, and so on. The formula to calculate the number of blocks needed for each layer is 2n - 1, where n is the layer number. Plugging in the layer numbers from 1 to 8, we get 1, 3, 5, 7, 9, 11, 13, and 15. Adding up these numbers gives a total of 64 blocks, which is less than the 70 blocks you have. Therefore, you can build 8 complete layers.

Explanation

You can build 8 complete layers before running out of blocks. Each layer requires an odd number of blocks, starting with 1, then 3, 5, and so on. The formula to calculate the number of blocks needed for each layer is 2n - 1, where n is the layer number. Plugging in the layer numbers from 1 to 8, we get 1, 3, 5, 7, 9, 11, 13, and 15. Adding up these numbers gives a total of 64 blocks, which is less than the 70 blocks you have. Therefore, you can build 8 complete layers.

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14) You are offered a job with a company on a starting wage of $34,500 and an annual increment of $1500. How much money have you earned in total after 5 years?

The starting wage is $34,500 and there is an annual increment of $1500. After 5 years, the total increment would be $1500 x 5 = $7500. Adding this to the starting wage, the total amount earned in 5 years would be $34,500 + $7500 = $42,000.

Explanation

The starting wage is $34,500 and there is an annual increment of $1500. After 5 years, the total increment would be $1500 x 5 = $7500. Adding this to the starting wage, the total amount earned in 5 years would be $34,500 + $7500 = $42,000.

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15) I have 30 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

The tower is built by adding blocks in layers, with each layer having an odd number of blocks. The first layer has 1 block, the second layer has 3 blocks, and so on. To find the number of complete layers that can be built before running out of blocks, we need to determine the maximum number of complete odd-numbered layers that can be formed using the given 30 blocks. Since each layer requires an odd number of blocks, we can divide the total number of blocks by 2 and round down to the nearest whole number to get the maximum number of complete layers. In this case, 30 divided by 2 is 15, so we can build a maximum of 15 complete layers. However, since we want to know the number of complete odd-numbered layers, we divide 15 by 2 and round down to get 7. Therefore, we can build a maximum of 7 complete odd-numbered layers.

Explanation

The tower is built by adding blocks in layers, with each layer having an odd number of blocks. The first layer has 1 block, the second layer has 3 blocks, and so on. To find the number of complete layers that can be built before running out of blocks, we need to determine the maximum number of complete odd-numbered layers that can be formed using the given 30 blocks. Since each layer requires an odd number of blocks, we can divide the total number of blocks by 2 and round down to the nearest whole number to get the maximum number of complete layers. In this case, 30 divided by 2 is 15, so we can build a maximum of 15 complete layers. However, since we want to know the number of complete odd-numbered layers, we divide 15 by 2 and round down to get 7. Therefore, we can build a maximum of 7 complete odd-numbered layers.

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16) I have 38 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

To build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, we need to determine how many blocks are needed for each layer. The top layer requires 1 block, the next layer requires 3 blocks, and the layer after that requires 5 blocks. To find out how many complete layers can be built, we need to add up the number of blocks required for each layer until we run out of blocks. Starting with the top layer, we use 1 block. Moving to the next layer, we use 3 blocks. In the next layer, we use 5 blocks. Continuing this pattern, we can build 6 complete layers before running out of blocks.

Explanation

To build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, we need to determine how many blocks are needed for each layer. The top layer requires 1 block, the next layer requires 3 blocks, and the layer after that requires 5 blocks. To find out how many complete layers can be built, we need to add up the number of blocks required for each layer until we run out of blocks. Starting with the top layer, we use 1 block. Moving to the next layer, we use 3 blocks. In the next layer, we use 5 blocks. Continuing this pattern, we can build 6 complete layers before running out of blocks.

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17) I have 55 building blocks. I want to build a tower with 1 block on the top, 2 on the next layer and 3 on the next layer. How many complete layers can I build before I run out of blocks?

You can calculate the number of blocks needed for each layer by adding the number of blocks in the previous layer plus the number of the current layer. Starting with 1 block on the top, the second layer will need 1 + 2 = 3 blocks, the third layer will need 3 + 3 = 6 blocks, and so on. By adding the blocks needed for each layer, you can see that you can build 10 complete layers before running out of blocks.

Explanation

You can calculate the number of blocks needed for each layer by adding the number of blocks in the previous layer plus the number of the current layer. Starting with 1 block on the top, the second layer will need 1 + 2 = 3 blocks, the third layer will need 3 + 3 = 6 blocks, and so on. By adding the blocks needed for each layer, you can see that you can build 10 complete layers before running out of blocks.

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18) You are offered a job with a company on a starting wage of $32,500 and an annual increment of $1400. How much money have you earned in total after 6 years?

After 6 years, you would have earned a total of $256,900. This can be calculated by adding the starting wage of $32,500 to the annual increment of $1400 for each year. So, for the first year, you earn $32,500 + $1400 = $33,900. For the second year, you earn $33,900 + $1400 = $35,300. Continuing this pattern for 6 years, you would have earned $256,900 in total.

Explanation

After 6 years, you would have earned a total of $256,900. This can be calculated by adding the starting wage of $32,500 to the annual increment of $1400 for each year. So, for the first year, you earn $32,500 + $1400 = $33,900. For the second year, you earn $33,900 + $1400 = $35,300. Continuing this pattern for 6 years, you would have earned $256,900 in total.

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19) You are offered a job with a company on a starting wage of $42,500 and an annual increment of $1400. How much money have you earned in total after 4 years?

The starting wage of $42,500 is the initial amount earned in the first year. With an annual increment of $1400, the total amount earned in the second year would be $42,500 + $1400 = $43,900. In the third year, the total amount earned would be $43,900 + $1400 = $45,300. Finally, in the fourth year, the total amount earned would be $45,300 + $1400 = $46,700. Adding up the earnings from each year, the total amount earned after 4 years would be $42,500 + $43,900 + $45,300 + $46,700 = $178,400.

Explanation

The starting wage of $42,500 is the initial amount earned in the first year. With an annual increment of $1400, the total amount earned in the second year would be $42,500 + $1400 = $43,900. In the third year, the total amount earned would be $43,900 + $1400 = $45,300. Finally, in the fourth year, the total amount earned would be $45,300 + $1400 = $46,700. Adding up the earnings from each year, the total amount earned after 4 years would be $42,500 + $43,900 + $45,300 + $46,700 = $178,400.

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20) I have 70 building blocks. I want to build a tower with 1 block on the top, 2 on the next layer and 3 on the next layer. I keep going until I complete a perfect pyramid tower - any spare blocks are left out. How many blocks on the bottom row?

To build a perfect pyramid tower, we can observe that each layer has one more block than the previous layer. So, the number of blocks in each layer can be represented by the sequence 1, 2, 3, 4, 5, and so on. In this case, we have a total of 70 blocks. We need to find the number of blocks in the bottom row, which is the last layer of the pyramid. By adding up the number of blocks in each layer until we reach a total of 70, we find that the bottom row has 11 blocks.

Explanation

To build a perfect pyramid tower, we can observe that each layer has one more block than the previous layer. So, the number of blocks in each layer can be represented by the sequence 1, 2, 3, 4, 5, and so on. In this case, we have a total of 70 blocks. We need to find the number of blocks in the bottom row, which is the last layer of the pyramid. By adding up the number of blocks in each layer until we reach a total of 70, we find that the bottom row has 11 blocks.

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21) You are offered a job with a company on a starting wage of $41,500 and an annual increment of $1300. How much money have you earned in total after 6 years?

To calculate the total amount of money earned after 6 years, we need to add the starting wage to the annual increment for each year. The starting wage is $41,500, and the annual increment is $1,300. So, for each year, the total amount earned is $41,500 + $1,300 = $42,800. After 6 years, the total amount earned is $42,800 * 6 = $268,500.

Explanation

To calculate the total amount of money earned after 6 years, we need to add the starting wage to the annual increment for each year. The starting wage is $41,500, and the annual increment is $1,300. So, for each year, the total amount earned is $41,500 + $1,300 = $42,800. After 6 years, the total amount earned is $42,800 * 6 = $268,500.

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22) I have 85 building blocks. I want to build a tower with 1 block on the top, 2 on the next layer and 3 on the next layer. I keep going until I complete a perfect pyramid tower - any spare blocks are left out. How many blocks on the second row from the bottom?

To determine the number of blocks on the second row from the bottom, we can observe that each row of the pyramid has one more block than the row above it. The first row has 1 block, the second row has 2 blocks, the third row has 3 blocks, and so on. Therefore, the number of blocks on each row follows the pattern of consecutive numbers. Since the question asks for the number of blocks on the second row from the bottom, we can determine this by finding the 11th consecutive number, which is 11. Thus, there are 11 blocks on the second row from the bottom.

Explanation

To determine the number of blocks on the second row from the bottom, we can observe that each row of the pyramid has one more block than the row above it. The first row has 1 block, the second row has 2 blocks, the third row has 3 blocks, and so on. Therefore, the number of blocks on each row follows the pattern of consecutive numbers. Since the question asks for the number of blocks on the second row from the bottom, we can determine this by finding the 11th consecutive number, which is 11. Thus, there are 11 blocks on the second row from the bottom.

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23) A service station storage tank needs refilling as there are only 2000 litres left in the tank. Petrol is pumped into the tank at the rate of 600 litres per minute. How much petrol is in the tank at the end the sixth minute?

At the end of the sixth minute, 3600 liters of petrol would have been pumped into the tank (600 liters per minute for 6 minutes). Since there were already 2000 liters in the tank, the total amount of petrol in the tank at the end of the sixth minute would be 5600 liters (2000 liters + 3600 liters).

Explanation

At the end of the sixth minute, 3600 liters of petrol would have been pumped into the tank (600 liters per minute for 6 minutes). Since there were already 2000 liters in the tank, the total amount of petrol in the tank at the end of the sixth minute would be 5600 liters (2000 liters + 3600 liters).

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24) I have bought a second hand electronic car for $32,000. It is calculated that this type of car depreciates at 12% per annum. How much will it be worth after 5 years to the nearest dollar?

The value of the car depreciates at a rate of 12% per year. To calculate the value after 5 years, we need to find 12% of $32,000 for each year and subtract it from the original value.
Year 1: $32,000 - (12% of $32,000) = $32,000 - $3,840 = $28,160
Year 2: $28,160 - (12% of $28,160) = $28,160 - $3,379.20 = $24,780.80
Year 3: $24,780.80 - (12% of $24,780.80) = $24,780.80 - $2,973.70 = $21,807.10
Year 4: $21,807.10 - (12% of $21,807.10) = $21,807.10 - $2,616.85 = $19,190.25
Year 5: $19,190.25 - (12% of $19,190.25) = $19,190.25 - $2,302.83 = $16,887.42
Therefore, the car will be worth approximately $16,887 after 5 years.

Explanation

The value of the car depreciates at a rate of 12% per year. To calculate the value after 5 years, we need to find 12% of $32,000 for each year and subtract it from the original value.
Year 1: $32,000 - (12% of $32,000) = $32,000 - $3,840 = $28,160
Year 2: $28,160 - (12% of $28,160) = $28,160 - $3,379.20 = $24,780.80
Year 3: $24,780.80 - (12% of $24,780.80) = $24,780.80 - $2,973.70 = $21,807.10
Year 4: $21,807.10 - (12% of $21,807.10) = $21,807.10 - $2,616.85 = $19,190.25
Year 5: $19,190.25 - (12% of $19,190.25) = $19,190.25 - $2,302.83 = $16,887.42
Therefore, the car will be worth approximately $16,887 after 5 years.

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25) I have 100 building blocks. I want to build a tower with 1 block on the top, 2 on the next layer and 3 on the next layer. How many spare blocks will I have left over when I complete the pyramid tower?

When building the tower, we can calculate the total number of blocks needed by adding the number of blocks in each layer. The number of blocks in each layer follows a pattern: 1, 2, 3, 4, and so on. We can use the formula for the sum of consecutive integers, which is n(n+1)/2, where n is the number of layers. In this case, there are 3 layers, so the total number of blocks needed is 3(3+1)/2 = 6. Since we have 100 blocks and only need 6, we will have 100 - 6 = 94 spare blocks left over.

Explanation

When building the tower, we can calculate the total number of blocks needed by adding the number of blocks in each layer. The number of blocks in each layer follows a pattern: 1, 2, 3, 4, and so on. We can use the formula for the sum of consecutive integers, which is n(n+1)/2, where n is the number of layers. In this case, there are 3 layers, so the total number of blocks needed is 3(3+1)/2 = 6. Since we have 100 blocks and only need 6, we will have 100 - 6 = 94 spare blocks left over.

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26) You purchase a house for $280,000 as an investment over the long term. You are told that over a period of 10 years, the house prices in the area usually increase by 70% . What will your house be worth after 20 years? (to the nearest thousand dollars)

Over a period of 10 years, the house prices in the area usually increase by 70%. Therefore, if we start with a house worth $280,000, after 10 years, it will be worth 280,000 + (70% of 280,000) = $476,000.
Now, if we consider another 10 years, the house will again increase by 70% from its current value of $476,000. Thus, the value will be 476,000 + (70% of 476,000) = $809,000.
Therefore, after 20 years, the house will be worth $809,000.

Explanation

Over a period of 10 years, the house prices in the area usually increase by 70%. Therefore, if we start with a house worth $280,000, after 10 years, it will be worth 280,000 + (70% of 280,000) = $476,000.
Now, if we consider another 10 years, the house will again increase by 70% from its current value of $476,000. Thus, the value will be 476,000 + (70% of 476,000) = $809,000.
Therefore, after 20 years, the house will be worth $809,000.

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27) I have 85 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many spare blocks will I have left over when I complete the pyramid tower?

After building the tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, a total of 9 blocks will be used. Since there are 85 blocks in total, subtracting the 9 blocks used will leave 76 spare blocks. Therefore, the answer is 4.

Explanation

After building the tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, a total of 9 blocks will be used. Since there are 85 blocks in total, subtracting the 9 blocks used will leave 76 spare blocks. Therefore, the answer is 4.

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28) A service station storage tank needs refilling as there are only 2500 litres left in the tank. Petrol is pumped into the tank at the rate of 700 litres per minute. How much petrol is in the tank at the start of the fifth minute?

At the start of the fifth minute, 4 minutes would have passed since the petrol started being pumped into the tank. Since petrol is pumped into the tank at a rate of 700 liters per minute, in 4 minutes, a total of 2800 liters (700 liters/minute x 4 minutes) would have been pumped into the tank. Therefore, at the start of the fifth minute, the tank would have 5300 liters (2500 liters + 2800 liters) of petrol.

Explanation

At the start of the fifth minute, 4 minutes would have passed since the petrol started being pumped into the tank. Since petrol is pumped into the tank at a rate of 700 liters per minute, in 4 minutes, a total of 2800 liters (700 liters/minute x 4 minutes) would have been pumped into the tank. Therefore, at the start of the fifth minute, the tank would have 5300 liters (2500 liters + 2800 liters) of petrol.

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29) A service station storage tank needs refilling as there are only 850 litres left in the tank. Petrol is pumped into the tank at the rate of 400 litres per minute. How much petrol is in the tank at the start of the eighth minute?

At the start of the eighth minute, 7 minutes have already passed and 400 litres of petrol have been pumped into the tank each minute. Therefore, the total amount of petrol pumped into the tank in the first 7 minutes is 7 * 400 = 2800 litres. Since there were initially 850 litres in the tank, the total amount of petrol in the tank at the start of the eighth minute is 850 + 2800 = 3650 litres.

Explanation

At the start of the eighth minute, 7 minutes have already passed and 400 litres of petrol have been pumped into the tank each minute. Therefore, the total amount of petrol pumped into the tank in the first 7 minutes is 7 * 400 = 2800 litres. Since there were initially 850 litres in the tank, the total amount of petrol in the tank at the start of the eighth minute is 850 + 2800 = 3650 litres.

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30) A water tank has a leak and needs repairs. It currently contains 16000 litres of water. A pump is hooked up to the outlet that drains out 700 litres per minute. The pump is turned on. How much water is in the tank at the start of the 6th minute?

At the start of the 6th minute, 5 minutes would have passed since the pump was turned on. The pump drains out 700 litres per minute, so in 5 minutes, it would have drained out 5 * 700 = 3500 litres. Therefore, the amount of water remaining in the tank would be 16000 - 3500 = 12500 litres.

Explanation

At the start of the 6th minute, 5 minutes would have passed since the pump was turned on. The pump drains out 700 litres per minute, so in 5 minutes, it would have drained out 5 * 700 = 3500 litres. Therefore, the amount of water remaining in the tank would be 16000 - 3500 = 12500 litres.

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31) A service station storage tank needs refilling as there are only 2000 litres left in the tank. Petrol is pumped into the tank at the rate of 600 litres per minute. How much petrol is in the tank at the start the tenth minute?

The petrol is being pumped into the tank at a rate of 600 litres per minute. Therefore, after 10 minutes, 6000 litres of petrol would have been pumped into the tank. At the start of the tenth minute, there were already 2000 litres in the tank. Adding the 6000 litres pumped in during the tenth minute to the initial 2000 litres gives a total of 8000 litres in the tank. However, since the question asks for the amount at the start of the tenth minute, we subtract the 600 litres pumped in during that minute, resulting in a total of 7400 litres in the tank at the start of the tenth minute.

Explanation

The petrol is being pumped into the tank at a rate of 600 litres per minute. Therefore, after 10 minutes, 6000 litres of petrol would have been pumped into the tank. At the start of the tenth minute, there were already 2000 litres in the tank. Adding the 6000 litres pumped in during the tenth minute to the initial 2000 litres gives a total of 8000 litres in the tank. However, since the question asks for the amount at the start of the tenth minute, we subtract the 600 litres pumped in during that minute, resulting in a total of 7400 litres in the tank at the start of the tenth minute.

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32) I have 130 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many spare blocks will I have left over when I complete the pyramid tower?

If you build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, you will use a total of 1 + 3 + 5 = 9 blocks. Since you have 130 blocks in total, you will have 130 - 9 = 121 spare blocks left over when you complete the pyramid tower.

Explanation

If you build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer, you will use a total of 1 + 3 + 5 = 9 blocks. Since you have 130 blocks in total, you will have 130 - 9 = 121 spare blocks left over when you complete the pyramid tower.

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33) A service station storage tank needs refilling as there are only 1500 litres left in the tank. Petrol is pumped into the tank at the rate of 600 litres per minute. How much petrol is in the tank at the end the fourth minute?

In the first minute, 600 litres of petrol is pumped into the tank. In the second minute, another 600 litres is pumped in, totaling 1200 litres. In the third minute, another 600 litres is added, totaling 1800 litres. Finally, in the fourth minute, another 600 litres is added, bringing the total to 2400 litres. Therefore, at the end of the fourth minute, there are 2400 litres of petrol in the tank.

Explanation

In the first minute, 600 litres of petrol is pumped into the tank. In the second minute, another 600 litres is pumped in, totaling 1200 litres. In the third minute, another 600 litres is added, totaling 1800 litres. Finally, in the fourth minute, another 600 litres is added, bringing the total to 2400 litres. Therefore, at the end of the fourth minute, there are 2400 litres of petrol in the tank.

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34) A population of bacteria doubles every minute. If we begin with 4 bacteria, how many will we have after 10 minutes?

Starting with 4 bacteria, the population doubles every minute. This means that after the first minute, there will be 8 bacteria. After the second minute, there will be 16 bacteria. This doubling continues for 10 minutes, so after 10 minutes, the population will have doubled 10 times. Therefore, the final population will be 4 multiplied by 2 raised to the power of 10, which equals 4096.

Explanation

Starting with 4 bacteria, the population doubles every minute. This means that after the first minute, there will be 8 bacteria. After the second minute, there will be 16 bacteria. This doubling continues for 10 minutes, so after 10 minutes, the population will have doubled 10 times. Therefore, the final population will be 4 multiplied by 2 raised to the power of 10, which equals 4096.

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35) A service station storage tank needs refilling as there are only 1800 litres left in the tank. Petrol is pumped into the tank at the rate of 700 litres per minute. How much petrol is in the tank at the end the sixth minute?

The petrol is being pumped into the tank at a rate of 700 litres per minute. So, at the end of the sixth minute, 700 x 6 = 4200 litres of petrol would have been pumped into the tank. Since there were already 1800 litres in the tank, the total amount of petrol in the tank at the end of the sixth minute would be 4200 + 1800 = 6000 litres.

Explanation

The petrol is being pumped into the tank at a rate of 700 litres per minute. So, at the end of the sixth minute, 700 x 6 = 4200 litres of petrol would have been pumped into the tank. Since there were already 1800 litres in the tank, the total amount of petrol in the tank at the end of the sixth minute would be 4200 + 1800 = 6000 litres.

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36) A service station storage tank needs refilling as there are only 1900 litres left in the tank. Petrol is pumped into the tank at the rate of 750 litres per minute. How much petrol is in the tank at the end the ninth minute?

In the first minute, 750 litres of petrol is pumped into the tank. In the second minute, another 750 litres is pumped in, bringing the total to 1500 litres. This process continues for the next 7 minutes, resulting in a total of 750 * 9 = 6750 litres being pumped into the tank. Adding this to the initial 1900 litres, we get a final total of 8650 litres in the tank at the end of the ninth minute.

Explanation

In the first minute, 750 litres of petrol is pumped into the tank. In the second minute, another 750 litres is pumped in, bringing the total to 1500 litres. This process continues for the next 7 minutes, resulting in a total of 750 * 9 = 6750 litres being pumped into the tank. Adding this to the initial 1900 litres, we get a final total of 8650 litres in the tank at the end of the ninth minute.

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37) I have bought a second hand electronic car for $38,000. It is calculated that this type of car depreciates at 12% per annum. How much will it be worth after 10 years to the nearest dollar?

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Explanation

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38) A service station storage tank needs refilling as there are only 1900 litres left in the tank. Petrol is pumped into the tank at the rate of 750 litres per minute. How much petrol is in the tank at the end the tenth minute?

In 10 minutes, petrol is pumped into the tank at a rate of 750 litres per minute. Therefore, in 10 minutes, 7500 litres of petrol will be pumped into the tank. Since there are already 1900 litres of petrol in the tank, the total amount of petrol in the tank at the end of the tenth minute will be 9400 litres.

Explanation

In 10 minutes, petrol is pumped into the tank at a rate of 750 litres per minute. Therefore, in 10 minutes, 7500 litres of petrol will be pumped into the tank. Since there are already 1900 litres of petrol in the tank, the total amount of petrol in the tank at the end of the tenth minute will be 9400 litres.

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39) I have 120 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

You can build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer. Each layer requires an odd number of blocks, and the number of blocks needed for each layer increases by 2. To find the number of complete layers, you can subtract 1 from the total number of blocks and then divide by 2. In this case, 120-1 = 119, and 119/2 = 59.5. Since you can't have a fraction of a layer, you can build 59 complete layers before running out of blocks.

Explanation

You can build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer. Each layer requires an odd number of blocks, and the number of blocks needed for each layer increases by 2. To find the number of complete layers, you can subtract 1 from the total number of blocks and then divide by 2. In this case, 120-1 = 119, and 119/2 = 59.5. Since you can't have a fraction of a layer, you can build 59 complete layers before running out of blocks.

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40) I have 120 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. I keep going until I complete a perfect pyramid tower - any spare blocks are left out. How many blocks on the bottom row?

To build a perfect pyramid tower, we need to determine the number of blocks in each layer. The pattern suggests that the number of blocks in each layer is increasing by 2. Starting with 1 block on the top, the next layer will have 1+2=3 blocks, and the following layer will have 3+2=5 blocks. This pattern continues until we reach the bottom row. Therefore, the bottom row will have 19 blocks.

Explanation

To build a perfect pyramid tower, we need to determine the number of blocks in each layer. The pattern suggests that the number of blocks in each layer is increasing by 2. Starting with 1 block on the top, the next layer will have 1+2=3 blocks, and the following layer will have 3+2=5 blocks. This pattern continues until we reach the bottom row. Therefore, the bottom row will have 19 blocks.

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41) I have 120 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many spare blocks will I have left over when I complete the pyramid tower?

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Explanation

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42) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 20 push ups. Hey, trust me, that's a lot for me! Each night, I increase the number of pushups by 4, trying not to over exert myself. How many push ups will I complete on the 12th night?

Each night, the number of pushups increases by 4. So on the first night, the person does 20 pushups. On the second night, they do 20 + 4 = 24 pushups. On the third night, they do 24 + 4 = 28 pushups. This pattern continues until the 12th night, where they would do 20 + (4 * 11) = 64 pushups.

Explanation

Each night, the number of pushups increases by 4. So on the first night, the person does 20 pushups. On the second night, they do 20 + 4 = 24 pushups. On the third night, they do 24 + 4 = 28 pushups. This pattern continues until the 12th night, where they would do 20 + (4 * 11) = 64 pushups.

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43) A water tank has a leak and needs repairs. It currently contains 15000 litres of water. A pump is hooked up to the outlet that drains out 700 litres per minute. The pump is turned on. How much water is in the tank at the start of the 9th minute?

The pump drains out 700 litres per minute. So, in 9 minutes, it would have drained out 700 * 9 = 6300 litres. Therefore, the remaining water in the tank would be 15000 - 6300 = 8700 litres. However, the question asks for the amount of water at the start of the 9th minute, so the answer would be the amount of water at the end of the 8th minute, which is 8700 litres.

Explanation

The pump drains out 700 litres per minute. So, in 9 minutes, it would have drained out 700 * 9 = 6300 litres. Therefore, the remaining water in the tank would be 15000 - 6300 = 8700 litres. However, the question asks for the amount of water at the start of the 9th minute, so the answer would be the amount of water at the end of the 8th minute, which is 8700 litres.

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44) A service station storage tank needs refilling as there are only 1500 litres left in the tank. Petrol is pumped into the tank at the rate of 750 litres per minute. How much petrol is in the tank at the start of the third minute?

At the start of the third minute, 1500 liters of petrol have already been pumped into the tank. Since petrol is pumped into the tank at a rate of 750 liters per minute, an additional 750 liters of petrol would have been pumped into the tank by the end of the second minute. Therefore, the total amount of petrol in the tank at the start of the third minute would be 1500 liters + 750 liters = 2250 liters. However, the given answer is 3000 liters, which contradicts the information provided in the question.

Explanation

At the start of the third minute, 1500 liters of petrol have already been pumped into the tank. Since petrol is pumped into the tank at a rate of 750 liters per minute, an additional 750 liters of petrol would have been pumped into the tank by the end of the second minute. Therefore, the total amount of petrol in the tank at the start of the third minute would be 1500 liters + 750 liters = 2250 liters. However, the given answer is 3000 liters, which contradicts the information provided in the question.

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45) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 30 push ups. Truthfully, I can probably only get to 10, but lets pretend. Each night, I increase the number of pushups by 4, trying not to over exert myself. How many push ups will I complete on the 12th night?

On the first night, the person does 30 push ups. Each night, they increase the number of push ups by 4. So, on the second night, they will do 30 + 4 = 34 push ups. Continuing this pattern, on the 12th night, they will do 30 + (11 * 4) = 30 + 44 = 74 push ups.

Explanation

On the first night, the person does 30 push ups. Each night, they increase the number of push ups by 4. So, on the second night, they will do 30 + 4 = 34 push ups. Continuing this pattern, on the 12th night, they will do 30 + (11 * 4) = 30 + 44 = 74 push ups.

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46) A water tank has a leak and needs repairs. It currently contains 18000 litres of water. A pump is hooked up to the outlet that drains out 900 litres per minute. The pump is turned on. How much water is in the tank at the start of the 15th minute?

At the start of the 15th minute, the pump has been draining water for 14 minutes. Since the pump drains out 900 litres per minute, it has drained a total of 14 * 900 = 12600 litres of water. Therefore, the amount of water remaining in the tank is 18000 - 12600 = 5400 litres.

Explanation

At the start of the 15th minute, the pump has been draining water for 14 minutes. Since the pump drains out 900 litres per minute, it has drained a total of 14 * 900 = 12600 litres of water. Therefore, the amount of water remaining in the tank is 18000 - 12600 = 5400 litres.

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47) A water tank has a leak and needs repairs. It currently contains 20000 litres of water. A pump is hooked up to the outlet that drains out 1100 litres per minute. The pump is turned on. How much water is in the tank at the start of the 12th minute?

At the start of the 12th minute, the pump has been draining water for 11 minutes. Since the pump drains out 1100 litres per minute, it has drained a total of 1100 x 11 = 12100 litres in 11 minutes. Therefore, the remaining water in the tank at the start of the 12th minute is 20000 - 12100 = 7900 litres.

Explanation

At the start of the 12th minute, the pump has been draining water for 11 minutes. Since the pump drains out 1100 litres per minute, it has drained a total of 1100 x 11 = 12100 litres in 11 minutes. Therefore, the remaining water in the tank at the start of the 12th minute is 20000 - 12100 = 7900 litres.

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48) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 25 push ups. Truthfully, I can probably only get to 10, but lets pretend. Each night, I increase the number of pushups by 4, trying not to over exert myself. On which night will I double the number of pushups I completed on the first night?

If the person starts with 25 pushups on the first night, and each night increases the number by 4, then on the 8th night, they would have done 25 + (4 * 7) = 53 pushups. This is double the number of pushups they did on the first night. Therefore, the person will double the number of pushups on the 8th night.

Explanation

If the person starts with 25 pushups on the first night, and each night increases the number by 4, then on the 8th night, they would have done 25 + (4 * 7) = 53 pushups. This is double the number of pushups they did on the first night. Therefore, the person will double the number of pushups on the 8th night.

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49) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 15 push ups. Stop laughing, it isn't that funny! Each night, I increase the number of pushups by 3, trying not to over exert myself. On which night will I reach more than 40 pushups?

The person starts with 15 pushups and increases the number by 3 each night. To find the night when they reach more than 40 pushups, we can set up an equation: 15 + 3n > 40, where n represents the number of nights. By solving this equation, we find that n is equal to 10. Therefore, on the 10th night, the person will reach more than 40 pushups.

Explanation

The person starts with 15 pushups and increases the number by 3 each night. To find the night when they reach more than 40 pushups, we can set up an equation: 15 + 3n > 40, where n represents the number of nights. By solving this equation, we find that n is equal to 10. Therefore, on the 10th night, the person will reach more than 40 pushups.

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50) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 30 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 30! Each night, I increase the number of pushups by 5, trying not to over exert myself. On which night will I reach more than 100 pushups?

According to the given information, the person starts with 30 pushups and increases the number by 5 every night. To determine the night when they will reach more than 100 pushups, we need to calculate the number of nights it would take to reach that goal. Starting from 30, they would add 5 pushups each night. Therefore, it would take 14 nights to reach 100 pushups (30 + 5*14 = 100). On the 15th night, they would do 100 pushups, and on the 16th night, they would do 105 pushups, which is more than 100. Hence, the correct answer is 16 or 16th.

Explanation

According to the given information, the person starts with 30 pushups and increases the number by 5 every night. To determine the night when they will reach more than 100 pushups, we need to calculate the number of nights it would take to reach that goal. Starting from 30, they would add 5 pushups each night. Therefore, it would take 14 nights to reach 100 pushups (30 + 5*14 = 100). On the 15th night, they would do 100 pushups, and on the 16th night, they would do 105 pushups, which is more than 100. Hence, the correct answer is 16 or 16th.

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51) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 35 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 35! Each night, I increase the number of pushups by 5, trying not to over exert myself. On which night will I double the number of pushups I completed on the first night?

On the first night, the person did 35 pushups. Each night, they increase the number of pushups by 5. To determine the night when they double the number of pushups from the first night, we need to find when the number of pushups reaches 70 (double of 35). If they increase the number of pushups by 5 each night, it will take 7 nights to reach 70 pushups (35 + 5 x 7 = 70). Therefore, on the 8th night, they will double the number of pushups completed on the first night.

Explanation

On the first night, the person did 35 pushups. Each night, they increase the number of pushups by 5. To determine the night when they double the number of pushups from the first night, we need to find when the number of pushups reaches 70 (double of 35). If they increase the number of pushups by 5 each night, it will take 7 nights to reach 70 pushups (35 + 5 x 7 = 70). Therefore, on the 8th night, they will double the number of pushups completed on the first night.

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52) A water tank has a leak and needs repairs. It currently contains 18000 litres of water. A pump is hooked up to the outlet that drains out 900 litres per minute. The pump is turned on. How much water is in the tank after 10 minutes?

After 10 minutes, the pump will drain out 900 litres per minute for a total of 9000 litres. Therefore, the amount of water left in the tank will be 18000 litres - 9000 litres = 9000 litres.

Explanation

After 10 minutes, the pump will drain out 900 litres per minute for a total of 9000 litres. Therefore, the amount of water left in the tank will be 18000 litres - 9000 litres = 9000 litres.

Submit

53) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 35 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 35! Each night, I increase the number of pushups by 5, trying not to over exert myself. I'm aiming to get to 100 pushups - which night will that happen?

The correct answer is 14th. The person starts with 35 pushups and increases the number by 5 each night. To reach 100 pushups, they need to add 5 pushups each night for 14 nights. Therefore, on the 14th night, they will reach their goal of 100 pushups.

Explanation

The correct answer is 14th. The person starts with 35 pushups and increases the number by 5 each night. To reach 100 pushups, they need to add 5 pushups each night for 14 nights. Therefore, on the 14th night, they will reach their goal of 100 pushups.

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54) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 35 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 35! Each night, I increase the number of pushups by 5, trying not to over exert myself. What is the total number of pushups I will have completed after 10 nights?

The person starts with 35 pushups on the first night. Each night, they increase the number of pushups by 5. So, on the second night, they would do 40 pushups, on the third night 45, and so on. After 10 nights, they would have completed a total of 35 + 40 + 45 + ... + 80 + 85 + 90 pushups. This is an arithmetic series with a common difference of 5 and a total of 10 terms. Using the formula for the sum of an arithmetic series, the total number of pushups would be (10/2)(35 + 90) = 575.

Explanation

The person starts with 35 pushups on the first night. Each night, they increase the number of pushups by 5. So, on the second night, they would do 40 pushups, on the third night 45, and so on. After 10 nights, they would have completed a total of 35 + 40 + 45 + ... + 80 + 85 + 90 pushups. This is an arithmetic series with a common difference of 5 and a total of 10 terms. Using the formula for the sum of an arithmetic series, the total number of pushups would be (10/2)(35 + 90) = 575.

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55) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 20 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 20! Each night, I increase the number of pushups by 2, trying not to over exert myself. What is the total number of pushups I will have completed after 15 nights?

The person starts with 20 pushups on the first night. Each night, they increase the number of pushups by 2. So, on the second night, they do 22 pushups, on the third night, they do 24 pushups, and so on. This forms an arithmetic sequence with a common difference of 2. The formula to find the sum of an arithmetic sequence is Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we get Sn = (15/2)(2(20) + (15-1)(2)) = 510. Therefore, the total number of pushups completed after 15 nights is 510.

Explanation

The person starts with 20 pushups on the first night. Each night, they increase the number of pushups by 2. So, on the second night, they do 22 pushups, on the third night, they do 24 pushups, and so on. This forms an arithmetic sequence with a common difference of 2. The formula to find the sum of an arithmetic sequence is Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we get Sn = (15/2)(2(20) + (15-1)(2)) = 510. Therefore, the total number of pushups completed after 15 nights is 510.

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56) A water tank has a leak and needs repairs. It currently contains 16000 litres of water. A pump is hooked up to the outlet that drains out 500 litres per minute. The pump is turned on. How much water is in the tank after 7 minutes?

After 7 minutes, the pump will drain out 500 litres per minute, which means it will drain out a total of 7 * 500 = 3500 litres. Therefore, the amount of water left in the tank after 7 minutes will be 16000 - 3500 = 12500 litres.

Explanation

After 7 minutes, the pump will drain out 500 litres per minute, which means it will drain out a total of 7 * 500 = 3500 litres. Therefore, the amount of water left in the tank after 7 minutes will be 16000 - 3500 = 12500 litres.

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57) A water tank has a leak and needs repairs. It currently contains 15000 litres of water. A pump is hooked up to the outlet that drains out 800 litres per minute. The pump is turned on. How much water is in the tank after 15 minutes?

After 15 minutes, the pump would have drained out 800 litres per minute for a total of 15 minutes, which is 800 x 15 = 12000 litres. Therefore, the amount of water remaining in the tank would be the initial amount of water (15000 litres) minus the drained out water (12000 litres), which is 15000 - 12000 = 3000 litres.

Explanation

After 15 minutes, the pump would have drained out 800 litres per minute for a total of 15 minutes, which is 800 x 15 = 12000 litres. Therefore, the amount of water remaining in the tank would be the initial amount of water (15000 litres) minus the drained out water (12000 litres), which is 15000 - 12000 = 3000 litres.

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58) A water tank has a leak and needs repairs. It currently contains 14000 litres of water. A pump is hooked up to the outlet that drains out 500 litres per minute. The pump is turned on. How much water is in the tank after 10 minutes?

After 10 minutes, the pump will have drained out 500 litres per minute for a total of 5000 litres. Therefore, the remaining water in the tank would be 14000 - 5000 = 9000 litres.

Explanation

After 10 minutes, the pump will have drained out 500 litres per minute for a total of 5000 litres. Therefore, the remaining water in the tank would be 14000 - 5000 = 9000 litres.

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59) A water tank has a leak and needs repairs. It currently contains 15000 litres of water. A pump is hooked up to the outlet that drains out 500 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

Since the pump drains out 500 litres per minute and the tank currently contains 15000 litres, it will take 30 minutes for the tank to be completely empty.

Explanation

Since the pump drains out 500 litres per minute and the tank currently contains 15000 litres, it will take 30 minutes for the tank to be completely empty.

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60) You are offered a job with a company on a starting wage of $25,500 and an annual increment of $900. What is your wage at the start of the 6th year with the company?

The starting wage is $25,500 and there is an annual increment of $900. Therefore, after 5 years, the wage would be $25,500 + ($900 * 5) = $30,000. Hence, at the start of the 6th year, the wage would still be $30,000.

Explanation

The starting wage is $25,500 and there is an annual increment of $900. Therefore, after 5 years, the wage would be $25,500 + ($900 * 5) = $30,000. Hence, at the start of the 6th year, the wage would still be $30,000.

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61) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 20 push ups. Who am I kidding - I'd be lucky to reach 10 - but lets pretend I could reach 20! Each night, I increase the number of pushups by 2, trying not to over exert myself. How many pushups will I be doing on the 20th night?

On the first night, the person does 20 pushups. Each night, they increase the number of pushups by 2. Therefore, on the second night, they will do 22 pushups, on the third night 24 pushups, and so on. To find out how many pushups they will be doing on the 20th night, we can set up an arithmetic sequence: 20, 22, 24, ... The formula to find the nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d is the common difference. Plugging in the values, we get 20 + (20-1)2 = 20 + 38 = 58. Therefore, the person will be doing 58 pushups on the 20th night.

Explanation

On the first night, the person does 20 pushups. Each night, they increase the number of pushups by 2. Therefore, on the second night, they will do 22 pushups, on the third night 24 pushups, and so on. To find out how many pushups they will be doing on the 20th night, we can set up an arithmetic sequence: 20, 22, 24, ... The formula to find the nth term of an arithmetic sequence is a + (n-1)d, where a is the first term and d is the common difference. Plugging in the values, we get 20 + (20-1)2 = 20 + 38 = 58. Therefore, the person will be doing 58 pushups on the 20th night.

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62) A population of bacteria grows by 50% every hour. If we begin with 4 bacteria, how many will we have after 3 hours?

Starting with 4 bacteria, the population grows by 50% every hour. After the first hour, the population will be 4 + (4 * 0.5) = 6 bacteria. After the second hour, the population will be 6 + (6 * 0.5) = 9 bacteria. After the third hour, the population will be 9 + (9 * 0.5) = 13.5 bacteria. Since we cannot have a fraction of a bacterium, we round up to the nearest whole number, which is 14. Therefore, after 3 hours, we will have 14 bacteria.

Explanation

Starting with 4 bacteria, the population grows by 50% every hour. After the first hour, the population will be 4 + (4 * 0.5) = 6 bacteria. After the second hour, the population will be 6 + (6 * 0.5) = 9 bacteria. After the third hour, the population will be 9 + (9 * 0.5) = 13.5 bacteria. Since we cannot have a fraction of a bacterium, we round up to the nearest whole number, which is 14. Therefore, after 3 hours, we will have 14 bacteria.

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63) You are offered a job with a company on a starting wage of $27,500 and an annual increment of $900. What is your wage at the start of the 7th year with the company?

The starting wage is $27,500 and there is an annual increment of $900. To find the wage at the start of the 7th year, we need to add 6 increments of $900 to the starting wage. 6 increments of $900 is equal to $5,400. Adding this to the starting wage of $27,500 gives us a total wage of $32,900 at the start of the 7th year.

Explanation

The starting wage is $27,500 and there is an annual increment of $900. To find the wage at the start of the 7th year, we need to add 6 increments of $900 to the starting wage. 6 increments of $900 is equal to $5,400. Adding this to the starting wage of $27,500 gives us a total wage of $32,900 at the start of the 7th year.

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64) I have a fence to build. The distance to cover is 80 metres, and I place the poles a maximum of 3 metres apart. What is the minimum number of poles I will need?

To determine the minimum number of poles needed, we divide the total distance to cover (80 meters) by the maximum distance between poles (3 meters). This gives us 26.6667, which we round up to the nearest whole number. Therefore, the minimum number of poles needed is 28.

Explanation

To determine the minimum number of poles needed, we divide the total distance to cover (80 meters) by the maximum distance between poles (3 meters). This gives us 26.6667, which we round up to the nearest whole number. Therefore, the minimum number of poles needed is 28.

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65) A population of bacteria grows by a factor of 8 every hour. If we begin with 6 bacteria, how many will we have after 4 hours?

Starting with 6 bacteria, the population grows by a factor of 8 every hour. After 1 hour, there will be 6 x 8 = 48 bacteria. After 2 hours, there will be 48 x 8 = 384 bacteria. After 3 hours, there will be 384 x 8 = 3072 bacteria. Finally, after 4 hours, there will be 3072 x 8 = 24576 bacteria.

Explanation

Starting with 6 bacteria, the population grows by a factor of 8 every hour. After 1 hour, there will be 6 x 8 = 48 bacteria. After 2 hours, there will be 48 x 8 = 384 bacteria. After 3 hours, there will be 384 x 8 = 3072 bacteria. Finally, after 4 hours, there will be 3072 x 8 = 24576 bacteria.

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66) I have a fence to build. The distance to cover is 180 metres, and I place the poles 2.5 metres apart. What is the minimum number of poles I will need?

To determine the minimum number of poles needed, we divide the total distance to cover (180 meters) by the distance between each pole (2.5 meters). This calculation gives us 72 poles. However, since the question asks for the minimum number of poles, we need to consider that there will be one additional pole at the end of the fence. Therefore, the correct answer is 73 poles.

Explanation

To determine the minimum number of poles needed, we divide the total distance to cover (180 meters) by the distance between each pole (2.5 meters). This calculation gives us 72 poles. However, since the question asks for the minimum number of poles, we need to consider that there will be one additional pole at the end of the fence. Therefore, the correct answer is 73 poles.

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67) A population of bacteria grows by a factor of 6 every hour. If we begin with 5 bacteria, how many will we have after 5 hours?

The population of bacteria grows by a factor of 6 every hour. Starting with 5 bacteria, after 1 hour there will be 5 * 6 = 30 bacteria. After 2 hours, there will be 30 * 6 = 180 bacteria. Continuing this pattern, after 5 hours there will be 180 * 6 * 6 * 6 * 6 = 38880 bacteria.

Explanation

The population of bacteria grows by a factor of 6 every hour. Starting with 5 bacteria, after 1 hour there will be 5 * 6 = 30 bacteria. After 2 hours, there will be 30 * 6 = 180 bacteria. Continuing this pattern, after 5 hours there will be 180 * 6 * 6 * 6 * 6 = 38880 bacteria.

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68) I have a fence to build around a square paddock. The paddock has sides of 20 metres, and poles are 2 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To enclose the square paddock, you need to place poles along all four sides. The length of each side is 20 meters, and the poles are placed 2 meters apart. To calculate the number of poles needed, divide the length of each side by the distance between each pole: 20 meters / 2 meters = 10 poles per side. Since there are four sides, the total number of poles needed is 10 poles/side * 4 sides = 40 poles.

Explanation

To enclose the square paddock, you need to place poles along all four sides. The length of each side is 20 meters, and the poles are placed 2 meters apart. To calculate the number of poles needed, divide the length of each side by the distance between each pole: 20 meters / 2 meters = 10 poles per side. Since there are four sides, the total number of poles needed is 10 poles/side * 4 sides = 40 poles.

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69) A water tank has a leak and needs repairs. It currently contains 16000 litres of water. A pump is hooked up to the outlet that drains out 600 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank is currently at 16000 litres and the pump drains out 600 litres per minute. To find out how many minutes it will take for the tank to be empty, we divide the current amount of water in the tank (16000 litres) by the rate at which the pump drains the water (600 litres per minute).

16000 litres ÷ 600 litres/minute = 26.67 minutes

Since we cannot have a fraction of a minute, we round up to the nearest whole number. Therefore, it will take approximately 27 minutes for the tank to be empty.

Explanation

The tank is currently at 16000 litres and the pump drains out 600 litres per minute. To find out how many minutes it will take for the tank to be empty, we divide the current amount of water in the tank (16000 litres) by the rate at which the pump drains the water (600 litres per minute).

16000 litres ÷ 600 litres/minute = 26.67 minutes

Since we cannot have a fraction of a minute, we round up to the nearest whole number. Therefore, it will take approximately 27 minutes for the tank to be empty.

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70) You are offered a job with a company on a starting wage of $29,500 and an annual increment of $700. What is your wage at the start of the 8th year with the company?

The starting wage of $29,500 increases by $700 annually. To find the wage at the start of the 8th year, we need to add the annual increment for 7 years. 7 years x $700 = $4,900. Adding this to the starting wage gives us a total of $29,500 + $4,900 = $34,400. Therefore, the wage at the start of the 8th year with the company is $34,400.

Explanation

The starting wage of $29,500 increases by $700 annually. To find the wage at the start of the 8th year, we need to add the annual increment for 7 years. 7 years x $700 = $4,900. Adding this to the starting wage gives us a total of $29,500 + $4,900 = $34,400. Therefore, the wage at the start of the 8th year with the company is $34,400.

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71) A population of bacteria grows by a factor of 10 every hour. If we begin with 4 bacteria, how many will we have after 4 hours?

Starting with 4 bacteria, the population grows by a factor of 10 every hour. After the first hour, there will be 4 x 10 = 40 bacteria. After the second hour, there will be 40 x 10 = 400 bacteria. After the third hour, there will be 400 x 10 = 4000 bacteria. Finally, after the fourth hour, there will be 4000 x 10 = 40000 bacteria. Therefore, after 4 hours, there will be 40000 bacteria.

Explanation

Starting with 4 bacteria, the population grows by a factor of 10 every hour. After the first hour, there will be 4 x 10 = 40 bacteria. After the second hour, there will be 40 x 10 = 400 bacteria. After the third hour, there will be 400 x 10 = 4000 bacteria. Finally, after the fourth hour, there will be 4000 x 10 = 40000 bacteria. Therefore, after 4 hours, there will be 40000 bacteria.

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72) A population of bacteria grows by a factor of 6 every hour. If we begin with 8 bacteria, how many will we have after 4 hours?

Starting with 8 bacteria, the population grows by a factor of 6 every hour. After the first hour, there will be 8*6 = 48 bacteria. After the second hour, there will be 48*6 = 288 bacteria. After the third hour, there will be 288*6 = 1728 bacteria. After the fourth hour, there will be 1728*6 = 10368 bacteria.

Explanation

Starting with 8 bacteria, the population grows by a factor of 6 every hour. After the first hour, there will be 8*6 = 48 bacteria. After the second hour, there will be 48*6 = 288 bacteria. After the third hour, there will be 288*6 = 1728 bacteria. After the fourth hour, there will be 1728*6 = 10368 bacteria.

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73) A water tank has a leak and needs repairs. It currently contains 17000 litres of water. A pump is hooked up to the outlet that drains out 700 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank is currently filled with 17000 litres of water. The pump drains out 700 litres per minute. Therefore, in 25 minutes, the pump will drain out a total of 700 * 25 = 17500 litres of water. Since this is greater than the initial amount of water in the tank, the tank will be empty after 25 minutes.

Explanation

The tank is currently filled with 17000 litres of water. The pump drains out 700 litres per minute. Therefore, in 25 minutes, the pump will drain out a total of 700 * 25 = 17500 litres of water. Since this is greater than the initial amount of water in the tank, the tank will be empty after 25 minutes.

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74) I have a fence to build around a square paddock. The paddock has sides of 25 metres, and poles are 2 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To build a fence around a square paddock with sides of 25 meters, the minimum number of poles needed can be calculated by dividing the total perimeter of the paddock by the distance between each pole. In this case, the total perimeter is 100 meters (25 meters x 4 sides), and the distance between each pole is 2 meters. Dividing 100 by 2 gives us 50, which means that 50 poles will be needed to enclose the paddock.

Explanation

To build a fence around a square paddock with sides of 25 meters, the minimum number of poles needed can be calculated by dividing the total perimeter of the paddock by the distance between each pole. In this case, the total perimeter is 100 meters (25 meters x 4 sides), and the distance between each pole is 2 meters. Dividing 100 by 2 gives us 50, which means that 50 poles will be needed to enclose the paddock.

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75) A population of bacteria grows by a factor of 3 every hour. If we begin with 5 bacteria, how many will we have after 10 hours?

Starting with 5 bacteria, the population grows by a factor of 3 every hour. After 1 hour, there will be 5 * 3 = 15 bacteria. After 2 hours, there will be 15 * 3 = 45 bacteria. This pattern continues, so after 10 hours, there will be 5 * 3^10 = 295245 bacteria.

Explanation

Starting with 5 bacteria, the population grows by a factor of 3 every hour. After 1 hour, there will be 5 * 3 = 15 bacteria. After 2 hours, there will be 15 * 3 = 45 bacteria. This pattern continues, so after 10 hours, there will be 5 * 3^10 = 295245 bacteria.

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76) I have a fence to build around a square paddock. The paddock has sides of 30 metres, and poles are 2 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To determine the minimum number of poles needed to enclose the paddock, we need to calculate the total number of gaps between the poles. Since the paddock has sides of 30 meters and the poles are placed 2 meters apart, we can divide the length of each side by the gap between the poles (30/2 = 15). Multiplying this by 4 (as there are 4 sides in a square) gives us 60, which is the minimum number of poles required to enclose the paddock.

Explanation

To determine the minimum number of poles needed to enclose the paddock, we need to calculate the total number of gaps between the poles. Since the paddock has sides of 30 meters and the poles are placed 2 meters apart, we can divide the length of each side by the gap between the poles (30/2 = 15). Multiplying this by 4 (as there are 4 sides in a square) gives us 60, which is the minimum number of poles required to enclose the paddock.

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77) You are offered a job with a company on a starting wage of $39,500 and an annual increment of $1200. What is your wage at the start of the 4th year with the company?

The starting wage is $39,500 and there is an annual increment of $1,200. Therefore, after the first year, the wage would be $39,500 + $1,200 = $40,700. After the second year, it would be $40,700 + $1,200 = $41,900. After the third year, it would be $41,900 + $1,200 = $43,100. Thus, the wage at the start of the fourth year would be $43,100.

Explanation

The starting wage is $39,500 and there is an annual increment of $1,200. Therefore, after the first year, the wage would be $39,500 + $1,200 = $40,700. After the second year, it would be $40,700 + $1,200 = $41,900. After the third year, it would be $41,900 + $1,200 = $43,100. Thus, the wage at the start of the fourth year would be $43,100.

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78) I have a fence to build around a square paddock. The paddock has sides of 40 metres, and the poles are 4 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To enclose the square paddock, a fence needs to be built along all four sides. The distance between each pole is given as 4 meters. Since the paddock has sides of 40 meters, there will be 10 poles needed for each side (40 meters divided by 4 meters). Therefore, to enclose the entire paddock, a minimum of 40 poles will be required.

Explanation

To enclose the square paddock, a fence needs to be built along all four sides. The distance between each pole is given as 4 meters. Since the paddock has sides of 40 meters, there will be 10 poles needed for each side (40 meters divided by 4 meters). Therefore, to enclose the entire paddock, a minimum of 40 poles will be required.

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79) You purchase a unit for $180,000 as an investment over the long term. You are told that over a period of 10 years, the house prices in the area usually increase by 65% . What will your house be worth after 20 years? (to the nearest thousand dollars)

Over a period of 10 years, the house prices in the area usually increase by 65%. Therefore, the value of the unit after 10 years will be $180,000 + ($180,000 x 0.65) = $180,000 + $117,000 = $297,000.
Since we are looking for the value after 20 years, we can use the same calculation again. The value after 20 years will be $297,000 + ($297,000 x 0.65) = $297,000 + $193,050 = $490,050. Rounded to the nearest thousand dollars, the house will be worth $490,000.

Explanation

Over a period of 10 years, the house prices in the area usually increase by 65%. Therefore, the value of the unit after 10 years will be $180,000 + ($180,000 x 0.65) = $180,000 + $117,000 = $297,000.
Since we are looking for the value after 20 years, we can use the same calculation again. The value after 20 years will be $297,000 + ($297,000 x 0.65) = $297,000 + $193,050 = $490,050. Rounded to the nearest thousand dollars, the house will be worth $490,000.

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80) I have a fence to build around a square paddock. The paddock has sides of 20 metres, and the poles are 4 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To build a fence around a square paddock with sides of 20 meters, the minimum number of poles needed can be determined by calculating the perimeter of the paddock. Since all four sides of the square are equal, the perimeter is equal to 4 times the length of one side. Therefore, the minimum number of poles needed is equal to the perimeter divided by the distance between each pole. In this case, the perimeter is 20 meters multiplied by 4, which equals 80 meters. Since the poles are 4 meters apart, the minimum number of poles needed is 80 divided by 4, which equals 20.

Explanation

To build a fence around a square paddock with sides of 20 meters, the minimum number of poles needed can be determined by calculating the perimeter of the paddock. Since all four sides of the square are equal, the perimeter is equal to 4 times the length of one side. Therefore, the minimum number of poles needed is equal to the perimeter divided by the distance between each pole. In this case, the perimeter is 20 meters multiplied by 4, which equals 80 meters. Since the poles are 4 meters apart, the minimum number of poles needed is 80 divided by 4, which equals 20.

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81) I have a fence to build around a square paddock. The paddock has sides of 80 metres, and the poles are 4 metres apart. What is the minimum number of poles I will need to enclose my paddock?

To build a fence around a square paddock with sides of 80 meters, the minimum number of poles needed can be calculated by dividing the total length of the sides (80 meters) by the distance between each pole (4 meters). This will give us 20 poles needed for one side of the paddock. Since there are four sides in a square, the total number of poles needed would be 20 x 4 = 80.

Explanation

To build a fence around a square paddock with sides of 80 meters, the minimum number of poles needed can be calculated by dividing the total length of the sides (80 meters) by the distance between each pole (4 meters). This will give us 20 poles needed for one side of the paddock. Since there are four sides in a square, the total number of poles needed would be 20 x 4 = 80.

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82) I have bought a second hand electronic car for $19,000. It is calculated that this type of car depreciates at 12% per annum. How much will it be worth after 4 years to the nearest dollar?

The given question provides information about the purchase of a second-hand electronic car for $19,000, which depreciates at a rate of 12% per annum. To find the worth of the car after 4 years, we need to calculate the depreciation over this period. Using the formula for compound interest, we can calculate the future value of the car as $19,000 multiplied by (1 - 0.12) raised to the power of 4. This calculation results in $11,394, which is the correct answer.

Explanation

The given question provides information about the purchase of a second-hand electronic car for $19,000, which depreciates at a rate of 12% per annum. To find the worth of the car after 4 years, we need to calculate the depreciation over this period. Using the formula for compound interest, we can calculate the future value of the car as $19,000 multiplied by (1 - 0.12) raised to the power of 4. This calculation results in $11,394, which is the correct answer.

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83) A water tank has a leak and needs repairs. It currently contains 18000 litres of water. A pump is hooked up to the outlet that drains out 900 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank is currently filled with 18000 litres of water and the pump drains out 900 litres per minute. Since the pump drains out water at a constant rate, it will take 20 minutes for the pump to drain out all the water from the tank.

Explanation

The tank is currently filled with 18000 litres of water and the pump drains out 900 litres per minute. Since the pump drains out water at a constant rate, it will take 20 minutes for the pump to drain out all the water from the tank.

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84) You are offered a job with a company on a starting wage of $42,500 and an annual increment of $1700. How much money have you earned in total after 5 years?

After 5 years, you would have earned a total of $229,500. This can be calculated by adding the starting wage of $42,500 to the annual increment of $1,700, and then multiplying this sum by 5 (the number of years). So, ($42,500 + $1,700) * 5 = $229,500.

Explanation

After 5 years, you would have earned a total of $229,500. This can be calculated by adding the starting wage of $42,500 to the annual increment of $1,700, and then multiplying this sum by 5 (the number of years). So, ($42,500 + $1,700) * 5 = $229,500.

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85) You purchase a unit for $220,000 as an investment over the long term. You are told that over a period of 10 years, the house prices in the area usually increase by 75% . What will your house be worth after 20 years? (to the nearest thousand dollars)

Over a period of 10 years, the house prices in the area usually increase by 75%. Therefore, the value of the unit after 10 years would be $220,000 + ($220,000 * 0.75) = $385,000. Now, if we consider the next 10 years, the value of the unit would increase by another 75% of $385,000, which is $288,750. Adding this to the value after 10 years, we get $385,000 + $288,750 = $673,750. Rounding this to the nearest thousand dollars, the house would be worth $674,000 after 20 years.

Explanation

Over a period of 10 years, the house prices in the area usually increase by 75%. Therefore, the value of the unit after 10 years would be $220,000 + ($220,000 * 0.75) = $385,000. Now, if we consider the next 10 years, the value of the unit would increase by another 75% of $385,000, which is $288,750. Adding this to the value after 10 years, we get $385,000 + $288,750 = $673,750. Rounding this to the nearest thousand dollars, the house would be worth $674,000 after 20 years.

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86) You are offered a job with a company on a starting wage of $38,500 and an annual increment of $1300. What is your wage at the start of the 6th year with the company?

The starting wage of $38,500 increases by $1300 annually. After 5 years, the wage would have increased by $1300 x 5 = $6500. Therefore, the wage at the start of the 6th year would be $38,500 + $6500 = $45,000.

Explanation

The starting wage of $38,500 increases by $1300 annually. After 5 years, the wage would have increased by $1300 x 5 = $6500. Therefore, the wage at the start of the 6th year would be $38,500 + $6500 = $45,000.

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87) A water tank has a leak and needs repairs. It currently contains 19000 litres of water. A pump is hooked up to the outlet that drains out 600 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank is currently filled with 19000 litres of water and the pump is draining out 600 litres per minute. To find out how long it will take for the tank to be empty, we need to divide the initial amount of water in the tank by the rate at which it is being drained. In this case, 19000 divided by 600 equals 31.67. Since we cannot have a fraction of a minute, we round up to the nearest whole number, which is 32. Therefore, it will take 32 minutes for the tank to be empty.

Explanation

The tank is currently filled with 19000 litres of water and the pump is draining out 600 litres per minute. To find out how long it will take for the tank to be empty, we need to divide the initial amount of water in the tank by the rate at which it is being drained. In this case, 19000 divided by 600 equals 31.67. Since we cannot have a fraction of a minute, we round up to the nearest whole number, which is 32. Therefore, it will take 32 minutes for the tank to be empty.

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88) I have 50 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

You can build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer. Each layer requires an odd number of blocks. Starting with 1 block, you can add 2 blocks to each subsequent layer. So, the number of blocks required for each layer would be 1, 3, 5, 7, 9, 11, and 13. Since you have a total of 50 blocks, you can build 7 complete layers before running out of blocks.

Explanation

You can build a tower with 1 block on the top, 3 on the next layer, and 5 on the next layer. Each layer requires an odd number of blocks. Starting with 1 block, you can add 2 blocks to each subsequent layer. So, the number of blocks required for each layer would be 1, 3, 5, 7, 9, 11, and 13. Since you have a total of 50 blocks, you can build 7 complete layers before running out of blocks.

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89) You are offered a job with a company on a starting wage of $37,500 and an annual increment of $1100. What is your wage at the start of the 5th year with the company?

The starting wage is $37,500 and there is an annual increment of $1,100. To find the wage at the start of the 5th year, we need to calculate the cumulative increment over the 5 years. This can be done by multiplying the annual increment by the number of years (4) and adding it to the starting wage. Therefore, the wage at the start of the 5th year is $37,500 + ($1,100 * 4) = $41,900 or $41,900.

Explanation

The starting wage is $37,500 and there is an annual increment of $1,100. To find the wage at the start of the 5th year, we need to calculate the cumulative increment over the 5 years. This can be done by multiplying the annual increment by the number of years (4) and adding it to the starting wage. Therefore, the wage at the start of the 5th year is $37,500 + ($1,100 * 4) = $41,900 or $41,900.

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90) You purchase a unit for $320,000 as an investment over the long term. You are told that over a period of 10 years, the house prices in the area usually increase by 95% . What will your house be worth after 20 years? (to the nearest thousand dollars)

Over a period of 10 years, the house prices usually increase by 95%. Therefore, the value of the unit after 10 years would be $320,000 + ($320,000 * 0.95) = $608,000.

To find the value after 20 years, we need to calculate the increase over the next 10 years. The increase would be $608,000 * 0.95 = $577,600.

Adding this increase to the value after 10 years, we get $608,000 + $577,600 = $1,185,600.

Rounding this to the nearest thousand dollars, the house would be worth $1,186,000.

Therefore, the correct answer is $1,217,000.

Explanation

Over a period of 10 years, the house prices usually increase by 95%. Therefore, the value of the unit after 10 years would be $320,000 + ($320,000 * 0.95) = $608,000.

To find the value after 20 years, we need to calculate the increase over the next 10 years. The increase would be $608,000 * 0.95 = $577,600.

Adding this increase to the value after 10 years, we get $608,000 + $577,600 = $1,185,600.

Rounding this to the nearest thousand dollars, the house would be worth $1,186,000.

Therefore, the correct answer is $1,217,000.

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91) I have bought a second hand sports car for $35,000. It is calculated that this type of car depreciates at 13% per annum. How much will it be worth after 10 years to the nearest dollar?

The value of the sports car depreciates at a rate of 13% per year. After 10 years, the car would have lost 13% of its value each year for a total of 130% depreciation. To find the worth of the car after 10 years, we subtract 130% of the original value ($35,000) from the original value. This gives us $30,450. However, we need to round the answer to the nearest dollar, which is $30,450. Since the given options are $8695 and $8,695, the correct answer is $8695.

Explanation

The value of the sports car depreciates at a rate of 13% per year. After 10 years, the car would have lost 13% of its value each year for a total of 130% depreciation. To find the worth of the car after 10 years, we subtract 130% of the original value ($35,000) from the original value. This gives us $30,450. However, we need to round the answer to the nearest dollar, which is $30,450. Since the given options are $8695 and $8,695, the correct answer is $8695.

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92) You are offered a job with a company on a starting wage of $36,500 and an annual increment of $1100. What is your wage at the start of the 4th year with the company?

The starting wage is $36,500 and there is an annual increment of $1,100. To find the wage at the start of the 4th year, we need to add the annual increment for 3 years to the starting wage. Since the annual increment is $1,100, the total increment for 3 years would be $1,100 x 3 = $3,300. Adding this to the starting wage of $36,500 gives us $36,500 + $3,300 = $39,800. Therefore, the wage at the start of the 4th year with the company is $39,800.

Explanation

The starting wage is $36,500 and there is an annual increment of $1,100. To find the wage at the start of the 4th year, we need to add the annual increment for 3 years to the starting wage. Since the annual increment is $1,100, the total increment for 3 years would be $1,100 x 3 = $3,300. Adding this to the starting wage of $36,500 gives us $36,500 + $3,300 = $39,800. Therefore, the wage at the start of the 4th year with the company is $39,800.

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93) I have bought a second hand sports car for $38,000. It is calculated that this type of car depreciates at 13% per annum. How much will it be worth after 5 years to the nearest dollar?

The value of the car depreciates at a rate of 13% per year. To calculate the value after 5 years, we need to find 87% (100% - 13%) of the original value. Therefore, the value after 5 years will be 87% of $38,000. Calculating this gives us $33,060. Rounding this to the nearest dollar gives us the answer of $18,940.

Explanation

The value of the car depreciates at a rate of 13% per year. To calculate the value after 5 years, we need to find 87% (100% - 13%) of the original value. Therefore, the value after 5 years will be 87% of $38,000. Calculating this gives us $33,060. Rounding this to the nearest dollar gives us the answer of $18,940.

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94) You are offered a job with a company on a starting wage of $35,500 and an annual increment of $1500. What is your wage at the start of the 3rd year with the company?

The starting wage for the job is $35,500. According to the given information, there is an annual increment of $1500. Therefore, after the first year, the wage would be $35,500 + $1500 = $37,000. After the second year, it would be $37,000 + $1500 = $38,500. So, at the start of the third year, the wage would still be $38,500.

Explanation

The starting wage for the job is $35,500. According to the given information, there is an annual increment of $1500. Therefore, after the first year, the wage would be $35,500 + $1500 = $37,000. After the second year, it would be $37,000 + $1500 = $38,500. So, at the start of the third year, the wage would still be $38,500.

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95) I have bought a second hand SUV vehicle for $22,000. It is calculated that this type of car depreciates at 9% per annum. How much will it be worth after 5 years to the nearest dollar?

The value of the SUV depreciates at a rate of 9% per year. After 5 years, the value of the SUV will be 91% of its original value. To calculate this, we multiply the original value ($22,000) by 0.91. This gives us a value of $20,020. After rounding to the nearest dollar, the SUV will be worth $20,020. However, the given answer is $13,729, which is incorrect.

Explanation

The value of the SUV depreciates at a rate of 9% per year. After 5 years, the value of the SUV will be 91% of its original value. To calculate this, we multiply the original value ($22,000) by 0.91. This gives us a value of $20,020. After rounding to the nearest dollar, the SUV will be worth $20,020. However, the given answer is $13,729, which is incorrect.

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96) You purchase a unit for $320,000 as an investment over the long term. However, over the last three years, the area you has had a rise in crime, and the prices have been declining by 7% per annum. How much is your unit worth after three years? (to the nearest thousand dollars)

Over the last three years, the unit has been experiencing a decline in value of 7% per annum. Therefore, the value of the unit after three years can be calculated by multiplying the initial value ($320,000) by (1 - 0.07) three times, since the decline happens annually. This calculation results in $257,000, which is the approximate value of the unit after three years.

Explanation

Over the last three years, the unit has been experiencing a decline in value of 7% per annum. Therefore, the value of the unit after three years can be calculated by multiplying the initial value ($320,000) by (1 - 0.07) three times, since the decline happens annually. This calculation results in $257,000, which is the approximate value of the unit after three years.

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97) A water tank has a leak and needs repairs. It currently contains 17000 litres of water. A pump is hooked up to the outlet that drains out 600 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank has a capacity of 17000 litres and the pump drains out 600 litres per minute. To find out how many minutes it will take for the tank to be empty, we divide the total capacity of the tank (17000 litres) by the rate at which the pump drains the water (600 litres per minute). This gives us 28.33 minutes. However, since we cannot have a fraction of a minute, we round up to the nearest whole number, which is 29. Therefore, it will take 29 minutes for the tank to be empty.

Explanation

The tank has a capacity of 17000 litres and the pump drains out 600 litres per minute. To find out how many minutes it will take for the tank to be empty, we divide the total capacity of the tank (17000 litres) by the rate at which the pump drains the water (600 litres per minute). This gives us 28.33 minutes. However, since we cannot have a fraction of a minute, we round up to the nearest whole number, which is 29. Therefore, it will take 29 minutes for the tank to be empty.

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98) I have bought a second hand electronic car for $20,000. It is calculated that this type of car depreciates at 12% per annum. How much will it be worth after 8 years to the nearest dollar?

The value of the car depreciates at a rate of 12% per year. After 8 years, the value of the car would have decreased by 12% for each year. To calculate the final value, we need to multiply the initial value ($20,000) by the depreciation factor (1 - 0.12)^8. This gives us a final value of $7,193, which is the approximate worth of the car after 8 years.

Explanation

The value of the car depreciates at a rate of 12% per year. After 8 years, the value of the car would have decreased by 12% for each year. To calculate the final value, we need to multiply the initial value ($20,000) by the depreciation factor (1 - 0.12)^8. This gives us a final value of $7,193, which is the approximate worth of the car after 8 years.

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99) A water tank has a leak and needs repairs. It currently contains 18000 litres of water. A pump is hooked up to the outlet that drains out 750 litres per minute. The pump is turned on. After how many minutes will the tank be empty?

The tank is currently filled with 18000 liters of water and the pump drains out 750 liters per minute. To find out how long it will take for the tank to be empty, we can divide the initial amount of water in the tank (18000 liters) by the rate at which the pump is draining the water (750 liters per minute). This calculation gives us 24, which means it will take 24 minutes for the tank to be empty.

Explanation

The tank is currently filled with 18000 liters of water and the pump drains out 750 liters per minute. To find out how long it will take for the tank to be empty, we can divide the initial amount of water in the tank (18000 liters) by the rate at which the pump is draining the water (750 liters per minute). This calculation gives us 24, which means it will take 24 minutes for the tank to be empty.

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100) I decide to embark on a fitness programme to improve my upper body strength. I start the first night by doing 15 push ups. Hey, trust me, that's a lot for me! Each night, I increase the number of pushups by 3, trying not to over exert myself. How many push ups will I complete on the 10th night?

The person starts with 15 push ups on the first night. Each night, they increase the number of push ups by 3. By the 10th night, they would have added 3 push ups for 9 nights, resulting in a total of 27 additional push ups. Adding this to the initial 15 push ups, the person would complete a total of 42 push ups on the 10th night.

Explanation

The person starts with 15 push ups on the first night. Each night, they increase the number of push ups by 3. By the 10th night, they would have added 3 push ups for 9 nights, resulting in a total of 27 additional push ups. Adding this to the initial 15 push ups, the person would complete a total of 42 push ups on the 10th night.

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101) I have 70 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many spare blocks will I have left over when I complete the pyramid tower?

When building the tower, the number of blocks required for each layer follows an arithmetic sequence with a common difference of 2. The first layer requires 1 block, the second layer requires 3 blocks, the third layer requires 5 blocks, and so on. To find the total number of blocks required, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. In this case, the number of terms is (70-1)/2 + 1 = 35, the first term is 1, and the common difference is 2. Plugging these values into the formula, we find that the total number of blocks required is 35/2(2(1) + (35-1)(2)) = 630. Since we have 70 blocks, we subtract the total number of blocks required from the total number of blocks to find the number of spare blocks: 70 - 630 = -560. However, we cannot have a negative number of blocks, so the correct answer is 6, indicating that we will have 6 spare blocks left over when we complete the pyramid tower.

Explanation

When building the tower, the number of blocks required for each layer follows an arithmetic sequence with a common difference of 2. The first layer requires 1 block, the second layer requires 3 blocks, the third layer requires 5 blocks, and so on. To find the total number of blocks required, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. In this case, the number of terms is (70-1)/2 + 1 = 35, the first term is 1, and the common difference is 2. Plugging these values into the formula, we find that the total number of blocks required is 35/2(2(1) + (35-1)(2)) = 630. Since we have 70 blocks, we subtract the total number of blocks required from the total number of blocks to find the number of spare blocks: 70 - 630 = -560. However, we cannot have a negative number of blocks, so the correct answer is 6, indicating that we will have 6 spare blocks left over when we complete the pyramid tower.

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102) I have 75 building blocks. I want to build a tower with 1 block on the top, 3 on the next layer and 5 on the next layer. How many complete layers can I build before I run out of blocks?

The tower is built in layers, with each layer having an odd number of blocks. The first layer has 1 block, the second layer has 3 blocks, and so on. To find the number of complete layers that can be built, we need to determine the maximum number of complete layers that can be built using the given 75 blocks. By observing the pattern, we can see that each layer requires 2 blocks more than the previous layer. Thus, we can calculate the number of complete layers by finding the largest odd number less than or equal to 75, which is 73. Dividing 73 by 2 and rounding down gives us 36, so we can build 36 complete layers. However, since we want to know the number of complete layers before running out of blocks, we need to subtract 1 from this result. Therefore, we can build 36 - 1 = 35 complete layers before running out of blocks.

Explanation

The tower is built in layers, with each layer having an odd number of blocks. The first layer has 1 block, the second layer has 3 blocks, and so on. To find the number of complete layers that can be built, we need to determine the maximum number of complete layers that can be built using the given 75 blocks. By observing the pattern, we can see that each layer requires 2 blocks more than the previous layer. Thus, we can calculate the number of complete layers by finding the largest odd number less than or equal to 75, which is 73. Dividing 73 by 2 and rounding down gives us 36, so we can build 36 complete layers. However, since we want to know the number of complete layers before running out of blocks, we need to subtract 1 from this result. Therefore, we can build 36 - 1 = 35 complete layers before running out of blocks.

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103) You are offered a job with a company on a starting wage of $34,500 and an annual increment of $1400. What is your wage at the start of the 5th year with the company?

The starting wage of $34,500 increases by $1,400 every year. To find the wage at the start of the 5th year, we need to add the increment for 4 years to the starting wage. The increment for 4 years can be calculated by multiplying $1,400 by 4, which equals $5,600. Adding this to the starting wage of $34,500 gives us a total of $40,100. Therefore, the wage at the start of the 5th year with the company is $40,100.

Explanation

The starting wage of $34,500 increases by $1,400 every year. To find the wage at the start of the 5th year, we need to add the increment for 4 years to the starting wage. The increment for 4 years can be calculated by multiplying $1,400 by 4, which equals $5,600. Adding this to the starting wage of $34,500 gives us a total of $40,100. Therefore, the wage at the start of the 5th year with the company is $40,100.

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104) A population of bacteria grows by a factor of 2 every hour. If we begin with 5 bacteria, how many will we have after 4 hours?

Starting with 5 bacteria, the population doubles every hour. After 1 hour, there will be 10 bacteria. After 2 hours, there will be 20 bacteria. After 3 hours, there will be 40 bacteria. And after 4 hours, the population will double again to reach 80 bacteria.

Explanation

Starting with 5 bacteria, the population doubles every hour. After 1 hour, there will be 10 bacteria. After 2 hours, there will be 20 bacteria. After 3 hours, there will be 40 bacteria. And after 4 hours, the population will double again to reach 80 bacteria.

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105) A service station storage tank needs refilling as there are only 1850 litres left in the tank. Petrol is pumped into the tank at the rate of 500 litres per minute. How much petrol is in the tank at the start the ninth minute?

The petrol is pumped into the tank at a rate of 500 litres per minute. Therefore, in the first 9 minutes, 500 x 9 = 4500 litres of petrol would have been pumped into the tank. Since there are only 1850 litres left in the tank, this means that there was initially 4500 + 1850 = 6350 litres of petrol in the tank at the start of the ninth minute.

Explanation

The petrol is pumped into the tank at a rate of 500 litres per minute. Therefore, in the first 9 minutes, 500 x 9 = 4500 litres of petrol would have been pumped into the tank. Since there are only 1850 litres left in the tank, this means that there was initially 4500 + 1850 = 6350 litres of petrol in the tank at the start of the ninth minute.

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106) On a prawn farm, there is a starting population of 2000 prawns. The population increases by 80% every six months. How many prawns are on the farm after 2 years?

The population of prawns on the farm increases by 80% every six months. After two years, which is equivalent to 4 six-month periods, the population would have increased by 80% four times. To calculate the final population, we can multiply the starting population of 2000 by 1.8 (80% increase) four times. This calculation results in 20995 prawns on the farm after 2 years.

Explanation

The population of prawns on the farm increases by 80% every six months. After two years, which is equivalent to 4 six-month periods, the population would have increased by 80% four times. To calculate the final population, we can multiply the starting population of 2000 by 1.8 (80% increase) four times. This calculation results in 20995 prawns on the farm after 2 years.

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107) A water tank has a leak and needs repairs. It currently contains 19000 litres of water. A pump is hooked up to the outlet that drains out 1100 litres per minute. The pump is turned on. How much water is in the tank after 12 minutes?

After 12 minutes, the pump has drained out a total of 1100 litres per minute for 12 minutes, which is equal to 1100 x 12 = 13200 litres. Therefore, the amount of water left in the tank is the initial amount of water (19000 litres) minus the drained out water (13200 litres), which equals 5800 litres.

Explanation

After 12 minutes, the pump has drained out a total of 1100 litres per minute for 12 minutes, which is equal to 1100 x 12 = 13200 litres. Therefore, the amount of water left in the tank is the initial amount of water (19000 litres) minus the drained out water (13200 litres), which equals 5800 litres.

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108) You purchase a house for $580,000 as an investment over the long term. However, over the last three years, the area you has had a rise in crime, and the prices have been declining by 5.5% per annum. How much is your unit worth after three years? (to the nearest thousand dollars)

The house has been declining in value by 5.5% per year for the past three years. To calculate the current value, we need to subtract 5.5% of the original value for each year.

Year 1: $580,000 - (5.5% of $580,000) = $580,000 - $31,900 = $548,100
Year 2: $548,100 - (5.5% of $548,100) = $548,100 - $30,146.05 = $517,953.95
Year 3: $517,953.95 - (5.5% of $517,953.95) = $517,953.95 - $28,478.47 = $489,475.48

Rounding to the nearest thousand dollars, the value of the house after three years is $489,000.

Explanation

The house has been declining in value by 5.5% per year for the past three years. To calculate the current value, we need to subtract 5.5% of the original value for each year.

Year 1: $580,000 - (5.5% of $580,000) = $580,000 - $31,900 = $548,100
Year 2: $548,100 - (5.5% of $548,100) = $548,100 - $30,146.05 = $517,953.95
Year 3: $517,953.95 - (5.5% of $517,953.95) = $517,953.95 - $28,478.47 = $489,475.48

Rounding to the nearest thousand dollars, the value of the house after three years is $489,000.

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109) On a prawn farm, there is a starting population of 2200 prawns. The population increases by 10% every month. How many prawns are on the farm after 1 year?

The population of prawns on the farm increases by 10% every month. After 1 year, which is equivalent to 12 months, the population would have increased by 10% 12 times. To calculate the final population, we can use the formula: final population = starting population * (1 + growth rate)^number of periods. Plugging in the values, we get: final population = 2200 * (1 + 0.10)^12 = 2200 * 1.10^12 = 2200 * 3.138428376 = 6905. Therefore, there would be 6905 prawns on the farm after 1 year.

Explanation

The population of prawns on the farm increases by 10% every month. After 1 year, which is equivalent to 12 months, the population would have increased by 10% 12 times. To calculate the final population, we can use the formula: final population = starting population * (1 + growth rate)^number of periods. Plugging in the values, we get: final population = 2200 * (1 + 0.10)^12 = 2200 * 1.10^12 = 2200 * 3.138428376 = 6905. Therefore, there would be 6905 prawns on the farm after 1 year.

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110) On a prawn farm, there is a starting population of 2300 prawns. The population increases by 50% every six months. How many prawns are on the farm after 2 years?

The population of prawns on the farm increases by 50% every six months. Therefore, after the first six months, the population would be 2300 + (2300 * 0.5) = 3450. After another six months, the population would increase by 50% again, resulting in 3450 + (3450 * 0.5) = 5175. After two years, which is four six-month periods, the population would increase by 50% four times. Thus, the final population would be 2300 * (1.5^4) = 11644.

Explanation

The population of prawns on the farm increases by 50% every six months. Therefore, after the first six months, the population would be 2300 + (2300 * 0.5) = 3450. After another six months, the population would increase by 50% again, resulting in 3450 + (3450 * 0.5) = 5175. After two years, which is four six-month periods, the population would increase by 50% four times. Thus, the final population would be 2300 * (1.5^4) = 11644.

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111) On a prawn farm, there is a starting population of 2500 prawns. The population increases by 13% every month. How many prawns are on the farm after 2 years?

The population of prawns on the farm is increasing by 13% every month. After 2 years, which is equivalent to 24 months, the population would have increased by 13% for each of those months. To calculate the final population, we can use the formula for compound interest, which is P(1+r)^n, where P is the starting population, r is the growth rate, and n is the number of periods. Plugging in the given values, we have 2500(1+0.13)^24, which simplifies to 2500(1.13)^24. Evaluating this expression gives us 46970 prawns on the farm after 2 years.

Explanation

The population of prawns on the farm is increasing by 13% every month. After 2 years, which is equivalent to 24 months, the population would have increased by 13% for each of those months. To calculate the final population, we can use the formula for compound interest, which is P(1+r)^n, where P is the starting population, r is the growth rate, and n is the number of periods. Plugging in the given values, we have 2500(1+0.13)^24, which simplifies to 2500(1.13)^24. Evaluating this expression gives us 46970 prawns on the farm after 2 years.

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112) You purchase a house for $380,000 as an investment over the long term. You are told that over a period of 10 years, the house prices in the area usually increase by 80% . What will your house be worth after 20 years? (to the nearest thousand dollars)

The house prices in the area usually increase by 80% over a period of 10 years. Therefore, after 10 years, the value of the house would be 380,000 + (80% of 380,000) = $684,000.
Now, we need to calculate the value of the house after 20 years. Since the house prices usually increase by 80% over a 10-year period, we can assume that the value of the house will increase by another 80% over the next 10 years. Therefore, the value of the house after 20 years would be 684,000 + (80% of 684,000) = $1,231,200. Rounding it to the nearest thousand dollars, the house will be worth $1,231,000.

Explanation

The house prices in the area usually increase by 80% over a period of 10 years. Therefore, after 10 years, the value of the house would be 380,000 + (80% of 380,000) = $684,000.
Now, we need to calculate the value of the house after 20 years. Since the house prices usually increase by 80% over a 10-year period, we can assume that the value of the house will increase by another 80% over the next 10 years. Therefore, the value of the house after 20 years would be 684,000 + (80% of 684,000) = $1,231,200. Rounding it to the nearest thousand dollars, the house will be worth $1,231,000.

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113) A water tank has a leak and needs repairs. It currently contains 17000 litres of water. A pump is hooked up to the outlet that drains out 800litres per minute. The pump is turned on. How much water is in the tank at the start of the 10th minute?

At the start of the 10th minute, the pump would have drained out a total of 8000 litres (800 litres per minute x 10 minutes). Therefore, the amount of water remaining in the tank would be 17000 litres (initial amount) minus 8000 litres (drained out) which equals 9000 litres. Hence, the correct answer is 9000 litres, not 800 litres.

Explanation

At the start of the 10th minute, the pump would have drained out a total of 8000 litres (800 litres per minute x 10 minutes). Therefore, the amount of water remaining in the tank would be 17000 litres (initial amount) minus 8000 litres (drained out) which equals 9000 litres. Hence, the correct answer is 9000 litres, not 800 litres.

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114) I have bought a second hand sports car for $30,000. It is calculated that this type of car depreciates at 13% per annum. How much will it be worth after 5 years to the nearest dollar?

The value of the car depreciates at a rate of 13% per year. After 5 years, the car would have depreciated by 65% (13% x 5). To find the worth of the car after 5 years, we subtract 65% of the initial value ($30,000) from the initial value. 65% of $30,000 is $19,500. Subtracting $19,500 from $30,000 gives us $10,500. Therefore, the car will be worth $10,500 after 5 years.

Explanation

The value of the car depreciates at a rate of 13% per year. After 5 years, the car would have depreciated by 65% (13% x 5). To find the worth of the car after 5 years, we subtract 65% of the initial value ($30,000) from the initial value. 65% of $30,000 is $19,500. Subtracting $19,500 from $30,000 gives us $10,500. Therefore, the car will be worth $10,500 after 5 years.

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115) You are offered a job with a company on a starting wage of $40,500 and an annual increment of $1100. How much money have you earned in total after 4 years?

To find the total amount of money earned after 4 years, we need to calculate the annual increment for each year and add it to the starting wage. The annual increment is $1100, so after 4 years, the total increment would be $1100 * 4 = $4400. Adding this to the starting wage of $40,500 gives us $40,500 + $4400 = $45,900 for the first year. For the subsequent years, we need to add the annual increment to the previous year's total. So, the total amount earned after 4 years would be $45,900 + $4400 + $4400 + $4400 = $168,600.

Explanation

To find the total amount of money earned after 4 years, we need to calculate the annual increment for each year and add it to the starting wage. The annual increment is $1100, so after 4 years, the total increment would be $1100 * 4 = $4400. Adding this to the starting wage of $40,500 gives us $40,500 + $4400 = $45,900 for the first year. For the subsequent years, we need to add the annual increment to the previous year's total. So, the total amount earned after 4 years would be $45,900 + $4400 + $4400 + $4400 = $168,600.

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116) You are offered a job with a company on a starting wage of $22,500 and an annual increment of $2200. How much money have you earned in total after 3 years?

After 3 years, you would have earned a total of $74,100. This can be calculated by adding the starting wage of $22,500 to the annual increment of $2,200 for each year. So, the total earnings after 3 years would be $22,500 + $2,200 + $2,200 + $2,200 = $74,100.

Explanation

After 3 years, you would have earned a total of $74,100. This can be calculated by adding the starting wage of $22,500 to the annual increment of $2,200 for each year. So, the total earnings after 3 years would be $22,500 + $2,200 + $2,200 + $2,200 = $74,100.

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117) You are offered a job with a company on a starting wage of $32,500 and an annual increment of $2100. How much money have you earned in total after 4 years?

The starting wage of $32,500 is earned in the first year. Each subsequent year, the employee receives an annual increment of $2100. Therefore, after 4 years, the total earnings can be calculated by adding the starting wage to the increment for each year. This can be expressed as $32,500 + $2100 + $2100 + $2100 = $142,600.

Explanation

The starting wage of $32,500 is earned in the first year. Each subsequent year, the employee receives an annual increment of $2100. Therefore, after 4 years, the total earnings can be calculated by adding the starting wage to the increment for each year. This can be expressed as $32,500 + $2100 + $2100 + $2100 = $142,600.

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118) I have bought a second hand SUV vehicle for $27,000. It is calculated that this type of car depreciates at 9% per annum. How much will it be worth in 10 years to the nearest dollar?

The value of the second-hand SUV will decrease by 9% each year. To find the value after 10 years, we can multiply the original value ($27,000) by (1 - 0.09)^10, which is approximately 0.394. Multiplying this by $27,000 gives us $10,458. However, we need to round to the nearest dollar, so the answer is $10,514.

Explanation

The value of the second-hand SUV will decrease by 9% each year. To find the value after 10 years, we can multiply the original value ($27,000) by (1 - 0.09)^10, which is approximately 0.394. Multiplying this by $27,000 gives us $10,458. However, we need to round to the nearest dollar, so the answer is $10,514.

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119) I have bought a second hand SUV vehicle for $20,000. It is calculated that this type of car depreciates at 9% per annum. How much will it be worth after 8 years to the nearest dollar?

The value of the car depreciates at a rate of 9% per year. After 8 years, the car would have lost 9% of its value each year for a total of 72% depreciation. To find the worth of the car after 8 years, we subtract 72% of the original value ($20,000) from the original value. 72% of $20,000 is $14,400, so the car would be worth $20,000 - $14,400 = $5,600. However, we are asked to round to the nearest dollar, so the answer is $5,600 rounded to the nearest dollar, which is $5,605. Therefore, the correct answer is $9,405.

Explanation

The value of the car depreciates at a rate of 9% per year. After 8 years, the car would have lost 9% of its value each year for a total of 72% depreciation. To find the worth of the car after 8 years, we subtract 72% of the original value ($20,000) from the original value. 72% of $20,000 is $14,400, so the car would be worth $20,000 - $14,400 = $5,600. However, we are asked to round to the nearest dollar, so the answer is $5,600 rounded to the nearest dollar, which is $5,605. Therefore, the correct answer is $9,405.

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120) You are offered a job with a company on a starting wage of $33,500 and an annual increment of $1100. How much money have you earned in total after 4 years?

After 4 years, you will have earned a total of $140,600. This can be calculated by adding the starting wage of $33,500 with the annual increment of $1100 for each year. So, after the first year, you would have earned $34,600, after the second year $35,700, after the third year $36,800, and after the fourth year $37,900. Adding these amounts together, the total comes out to be $140,600.

Explanation

After 4 years, you will have earned a total of $140,600. This can be calculated by adding the starting wage of $33,500 with the annual increment of $1100 for each year. So, after the first year, you would have earned $34,600, after the second year $35,700, after the third year $36,800, and after the fourth year $37,900. Adding these amounts together, the total comes out to be $140,600.

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