7th Grade Math Word Problems Quiz

1) Stephanie had $40.00 savings. Her mother gave her another $30.00 and her grandmother gave her $10.00 to buy a pair of cleats. The pair of cleats Stephanie wants costs $54.99. If Stephanie buys the cleats at a no TAX sale, write an equation using a variable to describe the amount of money that Stephanie will have to contribute from her savings. Solve for the variable.

$30.00 + $10.00 = $40.00 $40.00 + x = $54.99 x = $14.99

$30.00 + $10.00 = $40.00 $40.00 + x = $54.99 x = $15.00

Stephanie starts with $40.00 in savings. She receives additional amounts from her mother and grandmother:

Mother: $30.00

Grandmother: $10.00

The total amount she has available to spend on the cleats from these contributions and her savings is:

Total available=$40.00+$30.00+$10.00=$80.00

Problem

The cleats cost $54.99. We need to determine how much of her own savings Stephanie needs to contribute if the total amount she has is more than enough to cover the cost of the cleats.

Equation and Calculation

Let x represent the amount from her savings that Stephanie contributes to the purchase of the cleats.

We know that Stephanie has enough to cover the cost without needing to use all her savings:

x+$40.00=$54.99

Solving for x (the amount from her personal savings):

x=$54.99−$40.00=$14.99

Thus, Stephanie will need to contribute $14.99 from her savings to buy the cleats.

Explanation

Stephanie starts with $40.00 in savings. She receives additional amounts from her mother and grandmother:

Mother: $30.00

Grandmother: $10.00

The total amount she has available to spend on the cleats from these contributions and her savings is:

Total available=$40.00+$30.00+$10.00=$80.00

Problem

The cleats cost $54.99. We need to determine how much of her own savings Stephanie needs to contribute if the total amount she has is more than enough to cover the cost of the cleats.

Equation and Calculation

Let x represent the amount from her savings that Stephanie contributes to the purchase of the cleats.

We know that Stephanie has enough to cover the cost without needing to use all her savings:

x+$40.00=$54.99

Solving for x (the amount from her personal savings):

x=$54.99−$40.00=$14.99

Thus, Stephanie will need to contribute $14.99 from her savings to buy the cleats.

2) Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?

15kgs

18 kgs

20 kgs

10kgs

Given:

Three ducks and two ducklings weigh 32 kg.

Four ducks and three ducklings weigh 44 kg.

Let's denote the weight of one duck by

𝑑

d kg and the weight of one duckling by

𝑙

l kg.

From the problem, we can form the following equations:

3d+2l=32

4d+3l=44

We need to find the weight of two ducks and one duckling, which is represented as

2d+l.

First, solve the system of linear equations.

Multiply the first equation by 3 and the second equation by 2 to eliminate 𝑙

3(3d+2l)=3×32⟹9d+6l=96

2(4d+3l)=2×44⟹8d+6l=88

Subtract the second equation from the first:

9d+6l−(8d+6l)=96−88

9d−8d=8

d=8

Now substitute

d=8 into the first equation:

3(8)+2l=32

24+2l=32

2l=32−24

2l=8

l=4

We have

d=8 and

l=4.

Now, find the weight of two ducks and one duckling

2d+l:

2(8)+4=16+4=20

Therefore, the weight of two ducks and one duckling is

20 kg.

Explanation

Given:

Three ducks and two ducklings weigh 32 kg.

Four ducks and three ducklings weigh 44 kg.

Let's denote the weight of one duck by

𝑑

d kg and the weight of one duckling by

𝑙

l kg.

From the problem, we can form the following equations:

3d+2l=32

4d+3l=44

We need to find the weight of two ducks and one duckling, which is represented as

2d+l.

First, solve the system of linear equations.

Multiply the first equation by 3 and the second equation by 2 to eliminate 𝑙

3(3d+2l)=3×32⟹9d+6l=96

2(4d+3l)=2×44⟹8d+6l=88

Subtract the second equation from the first:

9d+6l−(8d+6l)=96−88

9d−8d=8

d=8

Now substitute

d=8 into the first equation:

3(8)+2l=32

24+2l=32

2l=32−24

2l=8

l=4

We have

d=8 and

l=4.

Now, find the weight of two ducks and one duckling

2d+l:

2(8)+4=16+4=20

Therefore, the weight of two ducks and one duckling is

20 kg.

3) The rent-a-stall horse barn has stalls for 1000 horses. Forty percent of the stalls are for ponies. On Tuesday, there were 200 ponies and a bunch of quarter horses at the horse barn. The horse barn was 75 percent full. How many quarter horses were in the stalls?

700 quarter horses

550 quarter horses

200 quarter horses

555 quarter horses

Explanation

4) A farmer grows 252 kilograms of apples. He sells them to a grocer who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses the same number of 5 kg bags as 2kg bags, then how many bags did he use in all?

72 bags

70 bags

60 bags

65 bags

Explanation

5) A 800 seat multiplex is divided into 3 theatres. There are 270 seats in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many seats are in Theatre 2?

300 seats

340 seats

210 seats

350 seats

Explanation

6) It takes one man one day to dig a 2m x 2m x 2m hole. How long does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?

2 1/2 days

2 2/3 days

1/2 day

1 7/8 days

First, let's determine the volume of the holes being dug.

The volume of the 2m x 2m x 2m hole:

V 1 =2×2×2=8 cubic meters

The volume of the 4m x 4m x 4m hole:

V 2 =4×4×4=64 cubic meters

We know that it takes one man one day to dig an 8 cubic meter hole. Therefore, one man digs at a rate of:

Rate of one man=8 cubic meters per day

Next, let's calculate the total work required to dig the 64 cubic meter hole.

The work required to dig a 64 cubic meter hole is:

Total work=64 cubic meters

Three men working together at the same rate will have a combined rate of:

Rate of three men=3×8=24 cubic meters per day

To find the time

t it takes for three men to dig the 64 cubic meter hole, we use the formula:

Time= Rate/Total work

Substituting the values:

𝑡 = 64 cubic meters / 24 cubic meters per day

= 64/24

= 8/3 days

Converting 8/3 into a mixed fraction:

8 ÷ 3 = 2 with a remainder of 2

8/3=2 2/3

Therefore, it takes three men days to dig a 4m x 4m x 4m hole.

Explanation

First, let's determine the volume of the holes being dug.

The volume of the 2m x 2m x 2m hole:

V 1 =2×2×2=8 cubic meters

The volume of the 4m x 4m x 4m hole:

V 2 =4×4×4=64 cubic meters

We know that it takes one man one day to dig an 8 cubic meter hole. Therefore, one man digs at a rate of:

Rate of one man=8 cubic meters per day

Next, let's calculate the total work required to dig the 64 cubic meter hole.

The work required to dig a 64 cubic meter hole is:

Total work=64 cubic meters

Three men working together at the same rate will have a combined rate of:

Rate of three men=3×8=24 cubic meters per day

To find the time

t it takes for three men to dig the 64 cubic meter hole, we use the formula:

Time= Rate/Total work

Substituting the values:

𝑡 = 64 cubic meters / 24 cubic meters per day

= 64/24

= 8/3 days

Converting 8/3 into a mixed fraction:

8 ÷ 3 = 2 with a remainder of 2

8/3=2 2/3

Therefore, it takes three men days to dig a 4m x 4m x 4m hole.

7) Mary has $50.00. She goes to the mall and buys lipstick and then she buys shampoo, which is half the price of the lipstick. She then spends half of what she has left on a purse, leaving her with $15.00. How much did the shampoo cost? How much did the lipstick cost?

$7.00; $15.00

$6.67; $13.33

$13.33; $6.67

$13.33 for both

Mary spends a certain amount on lipstick and half that amount on shampoo, then spends half of her remaining money on a purse, ending with $15.

Steps:

1. Initial and remaining money:

Start with $50.

After buying lipstick and shampoo, and then spending half of the remainder on a purse, she's left with $15.

2. Let x represent the cost of the lipstick; then shampoo costs x/2

3. Equation setup after purchasing and spending:

Money left after buying both: 50- x - x/2

Half of this amount is spent on purse, remaining is $15:

(50- x- x/2)/2 = 15

Solving this gives: 50 - x - x/2 = 30

50 - 1.5x=30

1.5x=20

x=20/1.5

x=$13.33

4. Cost of shampoo and final answer:

Shampoo costs x/2=13.33/2=6.67

ThereforeLipstick cost $13.33 and shampoo cost $6.67.

Explanation

Mary spends a certain amount on lipstick and half that amount on shampoo, then spends half of her remaining money on a purse, ending with $15.

Steps:

1. Initial and remaining money:

Start with $50.

After buying lipstick and shampoo, and then spending half of the remainder on a purse, she's left with $15.

2. Let x represent the cost of the lipstick; then shampoo costs x/2

3. Equation setup after purchasing and spending:

Money left after buying both: 50- x - x/2

Half of this amount is spent on purse, remaining is $15:

(50- x- x/2)/2 = 15

Solving this gives: 50 - x - x/2 = 30

50 - 1.5x=30

1.5x=20

x=20/1.5

x=$13.33

4. Cost of shampoo and final answer:

Shampoo costs x/2=13.33/2=6.67

ThereforeLipstick cost $13.33 and shampoo cost $6.67.

8) A rectangular chalk board is 3 times as long as it is wide. If it were 3 metres shorter and 3 metres wider, it would be square. What are the dimensions of the chalk board?

3 meters wide;9 meters long

2 meters wide;6 meters long

9 meters wide;3 meters long

6 meters wide;2 meters long

Explanation

9) Three people share a car for a period of one year and the mean number of kilometers travelled by each person is 152 per month. How many kilometers will be travelled in one year?

6049 km/year

6000 km/year

5500 km/year

5472 km/year

Explanation

10) In 1969 the price of 5 kilograms of flour was $0.75. In 1970 the price was increased 15 percent. In 1971, the 1970 price was decreased by 5 percent. What was the price of 5 kilograms of flour in 1971?

$0.90

$1.00

$0.86

$0.82

Explanation