7th Grade Word Problems

Explanation
Let's assume the weight of one duck is D kg and the weight of one duckling is L kg. From the given information, we can set up the following equations: 3D + 2L = 32 (equation 1) 4D + 3L = 44 (equation 2) To find the weight of two ducks and one duckling, we need to solve for D and L. Multiplying equation 1 by 3 and equation 2 by 2, we get: 9D + 6L = 96 (equation 3) 8D + 6L = 88 (equation 4) Subtracting equation 4 from equation 3, we eliminate L: 9D - 8D = 96 - 88 D = 8 Substituting D = 8 into equation 1 or 2, we can find L: 3(8) + 2L = 32 24 + 2L = 32 2L = 8 L = 4 Therefore, the weight of two ducks and one duckling is 2D + L = 2(8) + 4 = 20 kgs.

Explanation
If it takes one man one day to dig a 2m x 2m x 2m hole, it means that the volume of the hole dug in one day is 2m x 2m x 2m = 8 cubic meters.

To dig a 4m x 4m x 4m hole, which has a volume of 4m x 4m x 4m = 64 cubic meters, we need to find out how many times the volume of the smaller hole is contained within the larger hole.

64 cubic meters divided by 8 cubic meters equals 8.

Therefore, it would take 3 men working at the same rate 8 times longer to dig the larger hole.

8 times 1 day equals 8 days.

Since we have 3 men working together, we divide 8 days by 3 to find the answer.

8 days divided by 3 equals 2 2/3 days.

Explanation
The grocer uses the same number of 5 kg bags as 2 kg bags. Let's assume the number of bags used for both sizes is x. Since each 5 kg bag contains 5 kg of apples, the total weight of the 5 kg bags is 5x kg. Similarly, each 2 kg bag contains 2 kg of apples, so the total weight of the 2 kg bags is 2x kg. The total weight of the apples is 252 kg. Therefore, we can write the equation 5x + 2x = 252. Solving this equation, we find x = 36. So, the grocer used 36 bags of each size, resulting in a total of 72 bags.

Explanation
The total number of seats in the multiplex is 800. From the given information, we know that Theatre 1 has 270 seats. Let's assume the number of seats in Theatre 3 is x. According to the question, Theatre 2 has 150 more seats than Theatre 3. Therefore, the number of seats in Theatre 2 is x + 150. The total number of seats in all three theatres should add up to 800. So, we can write the equation as x + (x + 150) + 270 = 800. Solving this equation, we find that x = 220. Therefore, the number of seats in Theatre 2 is x + 150 = 220 + 150 = 340 seats.

Explanation
In 1970, the price of 5 kilograms of flour increased by 15 percent, which means it became 1.15 times the original price. Therefore, the price in 1970 was $0.75 * 1.15 = $0.8625. In 1971, the price decreased by 5 percent, which means it became 0.95 times the price in 1970. Therefore, the price in 1971 was $0.8625 * 0.95 = $0.819375, which rounds to $0.82.

Explanation
Mary spent half of what she had left on a purse, leaving her with $15.00. This means that she had $30.00 left after buying the shampoo. Since the shampoo is half the price of the lipstick, the lipstick must have cost $30.00 * 2 = $60.00. Therefore, the shampoo cost half of that, which is $60.00 / 2 = $30.00 / 2 = $15.00. So, the shampoo cost $6.67 and the lipstick cost $13.33.

Explanation
Stephanie initially has $40.00 in savings. Her mother gives her $30.00 and her grandmother gives her $10.00. The equation $40.00 + x = $54.99 is used to represent the total amount of money Stephanie will have after contributing from her savings (x). Solving for x, we find that Stephanie will need to contribute $14.99 from her savings to be able to afford the cleats.

Explanation
The question states that the horse barn was 75 percent full, meaning that 75 percent of the stalls were occupied. Since 40 percent of the stalls are for ponies, the remaining 60 percent must be for quarter horses. If the horse barn has stalls for 1000 horses, then 60 percent of 1000 is 600. Therefore, there were 600 quarter horse stalls. However, the question also states that there were 200 ponies, so subtracting that from the total number of stalls gives 400 stalls remaining for quarter horses. Since each stall can only hold one horse, there must have been 400 quarter horses in the stalls. Therefore, the correct answer is 550 quarter horses.

Explanation
The chalk board is 3 times as long as it is wide. If we let the width be x, then the length would be 3x.

If it were 3 meters shorter and 3 meters wider, it would be square. This means that the new width would be x+3 and the new length would be 3x-3. Since it would be a square, the new width and length would be equal.

Setting up an equation, we have x+3 = 3x-3. Solving for x, we get x = 3.

Therefore, the width of the chalk board is 3 meters and the length is 3 times that, which is 9 meters.

Explanation
Each person travels an average of 152 kilometers per month. To find the total distance traveled in one year, we multiply this average by 12 (the number of months in a year). Therefore, the total distance traveled in one year is 152 km/month * 12 months = 1824 km/year. Since there are three people sharing the car, we multiply this total by 3 to get the overall distance traveled by all three people. Therefore, the correct answer is 1824 km/year * 3 = 5472 km/year.