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2001 AMC 12 Problems/Problem 3

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Problem

The state income tax where Kristin lives is levied at the rate of p% of the first $28000 of annual income plus (p + 2)% of any amount above $28000. Kristin noticed that the state income tax she paid amounted to (p + 0.25)% of her annual income. What was her annual income?

\text{(A)}\,$28000\qquad \text{(B)}\,$32000\qquad \text{(C)}\,$35000\qquad \text{(D)}\,$42000\qquad \text{(E)}\,$56000

Solution

Let the income amount be denoted by A.

We know that \frac{A(p+.25)}{100}=\frac{28000p}{100}+\frac{(p+2)(A-28000)}{100}.

We can now try to solve for A:

(p+.25)A=28000p+Ap+2A-28000p-56000

.25A=2A-56000

A=32000

So the answer is \boxed{B}

See Also

2001 AMC 12 (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
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