Question

Kristin 所住州的所得税税率为：年收入前 $\$28000$ 按 $p\%$ 征税，超过 $\$28000$ 的部分按 $(p+2)\%$ 征税。Kristin 注意到她缴纳的州所得税等于年收入的 $(p+0.25)\%$ 。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：1370

解答：

设年收入为 $x\ge28000$ 。

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

两边乘以 $100$ 并展开，所有含 $p$ 的项抵消，得到 $2x-56000=0.25x$ 。因此 $1.75x=56000$ ，所以 $x=32000$ 。

所以正确答案是 B。

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 第 9 题

答案：B

难度评级：1370

解答：

其他年份的第 9 题