A pool measuring 10 feet by 20 feet will have a cement walkway around it. The area covered by the pool and the cement walkway is 600 square feet. If the walkway must have a uniform width around the entire pool, what is the width of the walkway?

Answer: the width of the walkway is 5 feet

Step-by-step explanation:

Let x represent the width of the walkway.

If the walkway must have a uniform width around the entire pool, it means that

The width of the total area would be x + 10 + x = 10 + 2x

The length of the total area would be x + 20 + x = 20 + 2x

The area covered by the pool and the cement walkway is 600 square feet. This means that

(10 + 2x) (20 + 2x) = 600

200 + 20x + 40x + 4x^2 = 600

4x^2 + 60x + 200 - 600 = 0

4x^2 + 60x - 400 = 0

Dividing through by 4, it becomes

x^2 + 15x - 100 = 0

x^2 + 20x - 5x - 100 = 0

x (x + 20) - 5 (x + 20) = 0

(x + 20) (x - 5) = 0

x = 5 or x = - 20

Since the width cannot be negative, then, the width of the walkway would be 5 feet on all sides.