Difference between revisions of "2001 AMC 10 Problems/Problem 9"

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== Problem ==
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Please navigate here for the solution: http://www.artofproblemsolving.com/Wiki/index.php/2001_AMC_12_Problems/Problem_3
 
 
The state income tax where Kristin lives is levied at the rate of <math> p\% </math> of the first <math> \</math><math>28000 </math> of annual income plus <math> (p + 2)\% </math> of any amount above <math> \</math><math>28000 </math>. Kristin noticed that the state income tax she paid amounted to <math> (p + 0.25)\% </math> of her annual income. What was her annual income?
 
 
 
<math> \textbf{(A) }\</math><math>28000\qquad\textbf{(B) }</math>\<math>32000\qquad\textbf{(C) }\</math><math>35000\qquad\textbf{(D) }</math>\<math>42,000\qquad\textbf{(E) }\</math><math>56000 </math>
 
 
 
== Solution ==
 
 
 
<math> 28000 \cdot \frac{p}{100}+(x-28000) \cdot \frac{p+2}{100}= \frac{p+0.25}{100}(x) </math>
 
 
 
<math> 280p+\frac{xp}{100}+\frac{x}{50}-280p-560 = \frac{xp}{100}+\frac{x}{400} </math>
 
 
 
<math> \frac{x}{50}-560 = \frac{x}{400} </math>
 
 
 
<math> 8x-(560)(400) = x </math>
 
 
 
<math> 7x = (560)(400) </math>
 
 
 
<math> x=(80)(400) </math>
 
 
 
<math> x = 32000 </math>
 
 
 
<math> \boxed{B} </math>.
 

Revision as of 15:10, 16 March 2011