Question

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?

$\$28000$

$\$32000$

$\$35000$

$\$42000$

$\$56000$

Answer: B

Concepts:percentage linear equation

Difficulty rating: 1370

Solution:

Let her income be $x\ge28000.$ Then

$\begin{aligned} &\tfrac{p}{100}(28000) \\ &\quad {}+\tfrac{p+2}{100}(x-28000) \\ &\quad =\tfrac{p+0.25}{100}x. \end{aligned}$

Multiplying by $100$ and expanding, all the $p$ terms cancel, leaving $2x-56000=0.25x.$ So $1.75x=56000$ and $x=32000.$

Thus, the correct answer is B.

2001 AMC 10 Problem 9

Answer: B

Difficulty rating: 1370

Solution:

Problem 9 in Other Years