2007 AMC 12B 第 10 题

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

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

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

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.

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