Difference between revisions of "2007 AMC 12B Problems/Problem 10"

Problem

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?

$\mathrm {(A)} 4$ $\mathrm {(B)} 6$ $\mathrm {(C)} 8$ $\mathrm {(D)} 10$ $\mathrm {(E)} 12$

Solution

First, determine the total number of people in the group.

$2=10/100t$

$t=200/10=20$

Now find the original number of girls:

$40/100t = 800/100 = 8$

So, there are 8 girls, $\Rightarrow \fbox{C}$