2007 AMC 10B Problem 14

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

The group size does not change when two leave and two arrive

The two departing girls represent

40\%-30\%

of the group

Two girls leave and two boys arrive, so the group size is unchanged. The two girls who left therefore represent

40\%-30\%=10\%

of the group.

Thus the group has

2\div 0.10=20

people, and the original number of girls was

40\%

of

20,

or

8.

Thus, the correct answer is C.

Problem 14 in other years