Question

The town swimming pool is d feet deep. The width of the pool is 10 feet greater than 5 times the depth. The length of the pool is 25 feet greater than the width.

A. Write and simplify an equation to represent the volume of the pool.
B. If the pool holds 51,000 cubic feet of water, what are the dimensions?

Answer 1

V = (d)(5d+10)(5d+35) which is 25d^3+225d^2+350d or if you factor out, it is 25d (d^2+9d+14 ) which can be further favored to 25d (d+7)(d+2).

Answer 2

A) The first thing you need to do in order to solve A is to know the formula for volume. It is length*width*depth (The * means that they are multiplied) The next part is to set up the equation in the volume formula. We need to have values for each the length, width, and depth. We know that the depth = d. The width will then be d*5+10. And the length will be d*5+10+25. In order to set up the full volume you will need to multiply each of these 3 equations together and simplify them.

B) Once you have simplified the answer to question A, you will need to set that equation equal to 51,000 ft^3. Then you can solve the problem using algebra to get the value of d. Once you have d you can plug the value into the equations for depth, width, and length to get the dimensions of the pool.

Hope this helped and good luck!