SOLUTION: You have an outdoor pool measuring 25 ft x 10 ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 cubic feet of cement, how w

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Question 808314: You have an outdoor pool measuring 25 ft x 10 ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 cubic feet of cement, how wide should the walkway be?
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
You have an outdoor pool measuring 25 ft x 10 ft. You want to add a cement walkway around the pool. If the walkway will be 1 ft thick and you have 304 cubic feet of cement, how wide should the walkway be?
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Area of the walkway of width w = (25+2w)*(10+2w) - 25*10
Area = 250 + 70w + 4w^2 - 250
= 4w^2 + 70w sq ft
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Vol = Area*depth
304 = 4w^2 + 70w
2w^2 + 35w - 152 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2441 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.60161932703562, -21.1016193270356. Here's your graph:

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w =~ 3.6 feet