Percentage Problem | AIME I, 2008 | Question 1

Of the students attending a 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, find number of students now at the party like to dance.

Let number of girls and boys be 3k and 2k, out of 3k girls, 2k likes to dance and 2k+20(boys) like to dance

here given that \(\frac{3k}{5k+20}\)=\(\frac{58}{100}\) then k=116

then 2k+20=252.

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