2001 AMC 12 Problems/Problem 3

Problem

The state income tax where Kristin lives is levied at the rate of $p%$ (Error compiling LaTeX. Unknown error_msg) of the first <dollar/> $28000$ of annual income plus $(p + 2)%$ (Error compiling LaTeX. Unknown error_msg) of any amount above <dollar/> $28000$ . Kristin noticed that the state income tax she paid amounted to $(p + 0.25)%$ (Error compiling LaTeX. Unknown error_msg) 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 $\boxed{B}$

2001 AMC 12 (Problems • Answer Key • Resources)
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

Page

Toolbox

Search

2001 AMC 12 Problems/Problem 3

Problem

Solution

See Also