2007 AMC 12B Problems/Problem 10

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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?

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

Solution

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

$2=(40/100-30/100)t$

$t=200/10=20$

Now find the original number of girls:

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

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

2007 AMC 12B (Problems • Resources)
Preceded by Problem 9	Followed by Problem 11
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2007 AMC 12B Problems/Problem 10

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