Question

一些男孩和女孩洗车，为去中国的班级旅行筹款。起初，女生占全组的 $40\%$ 。不久后两名女生离开，两名男生加入，此时女生占全组的 $30\%$ 。起初组里有多少名女生？

Some boys and girls are having a car wash to raise money for a class trip to China. Initially $40\%$ of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then $30\%$ of the group are girls. How many girls were initially in the group?

$4$

$6$

$8$

$10$

$12$

答案：C

知识点：百分数不变量

难度评级：1330

小提示：

两人离开、两人加入，所以总人数不变。

Two leave and two arrive, so the group size stays the same

大提示：

离开的两名女生对应女生比例下降的 $40\%-30\%=10\%$ 。

The two departing girls represent $40\%-30\%=10\%$ of the group

解答：

两名女生离开、两名男生加入，总人数不变，女生比例从 $40\%$ 降到 $30\%$ 。

下降的 $10\%$ 就对应这两名女生，所以全组有 $20$ 人，起初女生人数为 $20$ 的 $40\%$ ，即 $8$ 人。

所以正确答案是 C。

Since two girls leave while two boys arrive, the total group size is unchanged. The drop from $40\%$ to $30\%$ girls corresponds to the two girls who left.

So those two girls are $10\%$ of the group, meaning the group has $20$ people. The initial number of girls was $40\%$ of $20,$ or $8.$

Thus, the correct answer is C.

2007 AMC 12B 第 10 题

答案：C

难度评级：1330

小提示：

大提示：

解答：

其他年份的第 10 题