2007 AMC 12B Problem 10

Question

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

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

The two departing girls represent

40\%-30\%=10\%

of the group

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.

Problem 10 in other years