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6 November, 21:18

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?

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  1. 7 November, 00:32
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    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.
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