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

The following problem is from both the 2001 AMC 12 #3 and 2001 AMC 10 #9, so both problems redirect to this page.

## 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

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 $\boxed{B}$