math

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
get:

X = 1.083%, and x = 100%.

Solution: X = 1.08333%.

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3. OOPS! CORRECTION.

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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