An in ground rectangular pool has a concrete pathway surrounding the pool. if the pool is 16 feet by 32 feet and the entire area of the pool including the walkaway is 924 ft^2, find the width of the walkway

1. Let's call:

x: the width of the walkway.

b: 2x+16 (there is a widht "x" of the walkway on each side).

h: 2x+32 (there is a widht "x" of the walkway on each side).

A: 924 ft^2 (the area of the pool of including the walkway).

2. The area of a rectangle is:

A = (b) (h)

b: the base of the rectangle (2x+16)

a: the height of the rectangle (2x+32)

3. Then, we have a quadratic equation:

924 = (2x+16) (2x+32)

4x^2+64x+32x+512-924=0

4x^2+96x-412=0

4. We apply the quadratic formula to find the value of "x":

x = (-b±√ (b^2-4ac)) / 2a

x=3.71

The answer is: The width of the walkway is 3.71 ft