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: 1240

Solution:

Let her income be $x \gt 28000$ dollars. Writing the tax with both descriptions and multiplying by $100,$ $\begin{aligned} &p \cdot 28000 \\ &\quad {}+ (p + 2)(x - 28000) \\ &= (p + 0.25)x. \end{aligned}$

Expanding, every term containing $p$ cancels, leaving $2x - 56000 = 0.25x,$ so $1.75x = 56000$ and $x = 32000.$

Thus, the correct answer is B.

2001 AMC 12 Problem 3

Answer: B

Difficulty rating: 1240

Solution:

Problem 3 in Other Years