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2001 AMC 10 Problems/Problem 9

Revision as of 14:42, 16 March 2011 by Pidigits125 (talk | contribs) (→‎Solution)

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?

$\textbf{(A) }$$28000\qquad\textbf{(B) }$\$32000\qquad\textbf{(C) }$$35000\qquad\textbf{(D) }$\$42,000\qquad\textbf{(E) }$$56000$

Solution

$28000 \cdot \frac{p}{100}+(x-28000) \cdot \frac{p+2}{100}= \frac{p+0.25}{100}(x)$

$280p+\frac{xp}{100}+\frac{x}{50}-280p-560 = \frac{xp}{100}+\frac{x}{400}$

$\frac{x}{50}-560 = \frac{x}{400}$

$8x-(560)(400) = x$

$7x = (560)(400)$

$x=(80)(400)$

$x = 32000$ $\boxed{B}$.

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