2001 AMC 12 Problems/Problem 3

Revision as of 17:37, 16 March 2011 by Pidigits125 (talk | contribs)
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 $\boxed{B}$

See Also

2001 AMC 12 (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 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
2001 AMC 12 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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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