Question

一个大袋子里有 $500$ 个球，其中 $80\%$ 是红球，其余是蓝球。必须拿走多少个红球，才能使剩余球中 $75\%$ 是红球？

Of the $500$ balls in a large bag, $80\%$ are red and the rest are blue. How many of the red balls must be removed so that $75\%$ of the remaining balls are red?

$\ 25$

$\ 50$

$\ 75$

$\ 100$

$\ 150$

答案：D

知识点：百分数

难度评级：1120

解答：

若 $r$ 是红球数，则因此若 $b$ 是蓝球数，则 $r = 0.8\cdot500 = 400.$ $b = 500-400 = 100.$

拿走一些球后，如果红球占 $75\%$ ，那么蓝球占 $25\%$ 。蓝球数量不变，所以剩余球总数为 $\dfrac{100}{.25} = 400$ 。这表示总球数减少了 $500-400 = 100$ ，也就是拿走了一百个红球。

所以正确答案是 D。

If $r$ is the number of red balls, then $r = 0.8\cdot500 = 400.$ Therefore, if $b$ is the number of blue balls, then $b = 500-400 = 100.$

If there are $75\%$ red balls after removing balls, then there are $25\%$ blue balls. This means the total number of balls is $\dfrac{100}{.25} = 400.$ This means the total number of balls decreased by $500-400 = 100.$

Thus, the answer is D .

2010 AMC 8 第 12 题

答案：D

难度评级：1120

解答：

其他年份的第 12 题