2008 AIME I Problems/Problem 1

Problem

Of the students attending a school party, $60$ % of the students are girls, and $40$ % of the students like to dance. After these students are joined by $20$ more boy students, all of whom like to dance, the party is now $58$ % girls. How many students now at the party like to dance?

Solution

Say that there were $3k$ girls and $2k$ boys at the party originally. $2k$ like to dance. Then, there are $3k$ girls and $2k + 20$ boys, and $2k + 20$ like to dance.

Thus, $\dfrac{3k}{5k + 20} = \dfrac{29}{50}$ , solving gives $k = 116$ . Thus, the number of people that like to dance is $2k + 20 = \boxed{252}$ .

2008 AIME I (Problems • Answer Key • Resources)
Preceded by First question	Followed by Problem 2
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2008 AIME I Problems/Problem 1

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