Question

一所高中有 $500$ 名学生。 $40\%$ 的高年级学生会演奏乐器，而 $30\%$ 的非高年级学生不会演奏乐器。全校共有 $46.8\%$ 的学生不会演奏乐器。有多少非高年级学生会演奏乐器？

In a high school with $500$ students, $40\%$ of the seniors play a musical instrument, while $30\%$ of the non-seniors do not play a musical instrument. In all, $46.8\%$ of the students do not play a musical instrument. How many non-seniors play a musical instrument?

$66$

$154$

$186$

$220$

$266$

答案：B

知识点：百分数一次方程

难度评级：1120

解答：

设高年级学生人数为 $s$ 。则非高年级学生有 $500-s$ 人。高年级学生中 $60\%$ 不会演奏乐器。因此，不会演奏乐器的人数可表示为另一方面，所以非高年级学生有 $220$ 人，其中 $70\%$ 会演奏乐器，因此人数为 $\begin{aligned} &0.3(500-s)+0.6(s) \\ &= 0.3s+150 \end{aligned}$ $0.468\cdot 500=234.$ $0.3s+150=234$ $s=280.$ $220\cdot 0.7=154.$

所以答案是 B。

Let the number of seniors be $s.$ Then, $500-s$ people aren't seniors. We know $60\%$ of seniors don't play an instrument. Then, the number of students who don't play an instrument can be represented as $\begin{aligned} &0.3(500-s)+0.6(s) \\ &= 0.3s+150 \end{aligned}$ and $0.468\cdot 500=234.$ Thus, $0.3s+150=234$ $s=280.$ This makes the number of non-seniors equal to $220.$ Since $70\%$ of non-seniors play instruments, we have the total number as $220\cdot 0.7=154.$

Thus, the answer is B .

2019 AMC 10B 第 3 题

答案：B

难度评级：1120

解答：

其他年份的第 3 题