Question

An above-ground swimming pool contains 1024 cu. feet of water. The rectangular base of the pool is (x + 1) feet by y feet. The height of the water is 4 feet. What are the possible dimensions of the base of the pool? If one cubic foot of water weighs approximately 62.4 pounds, what is the total weight of the water in the pool?

Answer 1

To find the possible dimensions of the base of the pool, solve for x and y using the equation (x + 1) * y * 4 = 1024. The possible dimensions are (15, 16), (31, 8), and (63, 4). The total weight of the water in the pool is 63897.6 pounds.

Step-by-step explanation:

To find the possible dimensions of the base of the pool, we need to solve for x and y in the equation (x + 1) * y * 4 = 1024. Here's how:

1. Divide both sides of the equation by 4 to isolate the product of (x + 1) and y: (x + 1) * y = 256.

2. Find factors of 256 that work for (x + 1) and y. Possible pairs include (16, 16), (32, 8), and (64, 4).

3. Subtract 1 from each factor to get the dimensions of the base: (15, 16), (31, 8), and (63, 4).

The total weight of the water in the pool can be found by multiplying the volume of water (1024 cu. feet) by the weight of one cubic foot of water (62.4 pounds). So, the total weight is 1024 * 62.4 = 63897.6 pounds.