Question

Kristin 所住的州规定，年收入中前 $\$28000$ 的所得税率为 $p\%$ ，超过 $\$28000$ 的部分税率为 $(p + 2)\%$ 。Kristin 发现，她缴纳的州所得税相当于年收入的 $(p + 0.25)\%$ 。她的年收入是多少？

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?

$\$28000$

$\$32000$

$\$35000$

$\$42000$

$\$56000$

答案：B

知识点：百分数一次方程

难度评级：1240

解答：

设她的收入为 $x \gt 28000$ 美元。用两种描述写出税额，并同乘以 $100$ ， $\begin{aligned} &p \cdot 28000 \\ &\quad {}+ (p + 2)(x - 28000) \\ &= (p + 0.25)x. \end{aligned}$

展开后，所有含 $p$ 的项都抵消，剩下所以 $1.75x = 56000$ ，且 $x = 32000$ 。 $2x - 56000 = 0.25x,$

因此，正确答案是 B。

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 第 3 题

答案：B

难度评级：1240

解答：

其他年份的第 3 题