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A rectangular swimming pool is 60 ft wide and 80 ft long. A nonskid surface of uniform width is to be installed around the pool. If there is 576 ft^2 of the

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1 Answer

Hi Susana,
 
Let's start with the area of the pool itself, which we know is 60 x 80 = 4800 square feet. If we let the width of the nonskid surface be x, then the width of the pool + nonskid surface is 60 + 2x, and the length of the pool + nonskid surface is 80 + x. So, the total area of the pool including the nonskid surface is length x width, or (60 + 2x)((80+ 2x). The total area of the pool + nonskid surface minus the area of just the pool is the area of just the nonskid surface, or mathematically:
 
(60 + 2x)(80 + 2x) - 4800 = 576
 
After expanding, we have:
 
4800 + 160x + 120x + 4x^2 = 5376
 
Combining like terms gives:
 
4x^2 + 280x - 576 = 0
 
Dividing all terms by 4 gives:
 
x^2 + 70x - 144 = 0
 
This quadratic can be solved by factoring or with the quadratic formula. Factoring gives:
 
(x+72)(x-2) = 0
 
The solutions are then x = -72 and x = 2. We know the nonskid material cannot be -72 feet wide, so the only solution that makes sense is x = 2.
 
So the width is 2 feet.

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