The functionf(x) = 300x/100-x models the cost, F(x) in m illions of dollars to remove x% of a rivers pollutants. If the government commits $325 million for this project, what percentage of the pollutants can be removed?

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  1. I will assume you meant
    f(x) = 300x/(100-x)

    so if f(x) = 325
    325 = 300x/(100-x)
    32500 - 325x = 300x
    32500 = 625x
    x = 32500/625 = 52

    so 52% has been removed.

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  2. F(x) = 300X/(100-X) = $325M.

    300X/(100-X) = 325,
    Multiply both sides by 100-X:
    30000X - 300X^2 = 32500 - 325X,
    -300X^2 + 30000X + 325X-32,500 = 0,
    -300X^2 + 30,325X - 32,500 = 0,
    Divide both sides by -25:
    12X^2 - 1213 + 1300 = 0,
    Solve using the Quadratic Formula and

    X = 1.083%, and x = 100%.

    Solution: X = 1.08333%.

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    Multiply both sides by 100-X and get:
    300X = (100-X)325,
    300X = 32500 - 325X,
    300X + 325X = 32500,
    625X = 32500,
    X = 52%.

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