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

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==Problem==
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Some boys and girls are having a car wash to raise money for a class trip to China. Initially <math>40</math>% of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then <math>30</math>% of the group are girls. How many girls were initially in the group?
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<math>\mathrm {(A)} 4</math>  <math>\mathrm {(B)} 6</math>  <math>\mathrm {(C)} 8</math>  <math>\mathrm {(D)} 10</math>  <math>\mathrm {(E)} 12</math>
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==Solution==
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First, determine the total number of people in the group.
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<math>2=10/100t</math>
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<math>t=200/10=20</math>
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Now find the original number of girls:
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<math>40/100t = 800/100 = 8</math>
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So, there are 8 girls, <math>\Rightarrow \fbox{C}</math>

Revision as of 04:41, 1 September 2008

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, $\Rightarrow \fbox{C}$

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