Answer: The walkway should be 8.5 feet wide.
Step-by-step explanation: First, let's find the total area of the pool and the walkway. The pool measures 8 feet by 10 feet, so its area is:
8 ft x 10 ft = 80 ft²
The walkway will go around the pool, so it will add an equal amount to each side of the pool. If we let x represent the width of the walkway, then the length of the pool and walkway together will be:
10 ft + 2x (one width of the pool plus two widths of the walkway)
and the width of the pool and walkway together will be:
8 ft + 2x (one length of the pool plus two widths of the walkway)
So the total area of the pool and walkway will be:
(10 ft + 2x) x (8 ft + 2x) = 360 ft²
Expanding the left side of the equation, we get:
80 ft² + 20x ft² + 16x ft² + 4x² = 360 ft²
Combining like terms and simplifying, we get:
4x² + 36x - 280 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 4, b = 36, and c = -280, so:
x = (-36 ± sqrt(36² - 4(4)(-280))) / 8
x = (-36 ± sqrt(16976)) / 8
x = (-36 ± 130) / 8
We take only the positive value of x since it is a width. Thus, x = 8.5.
Therefore, the walkway should be 8.5 feet wide.