# Difference between revisions of "2001 AMC 12 Problems/Problem 3"

## Problem

The state income tax where Kristin lives is levied at the rate of $p%$ (Error compiling LaTeX. ! Missing $inserted.) of the first <dollar/> $28000$ of annual income plus$(p + 2)%$(Error compiling LaTeX. ! Missing$ inserted.) of any amount above <dollar/> $28000$. Kristin noticed that the state income tax she paid amounted to $(p + 0.25)%$ (Error compiling LaTeX. ! Missing \$ inserted.) of her annual income. What was her annual income? $\text{(A)}\,$<dollar/> $28000\qquad \text{(B)}\,$<dollar/> $32000\qquad \text{(C)}\,$<dollar/> $35000\qquad \text{(D)}\,$<dollar/> $42000\qquad \text{(E)}\,$<dollar/> $56000$

## Solution (unverified)

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 (Problems • Answer Key • Resources) Preceded byProblem 2 Followed byProblem 4 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 12 Problems and Solutions
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