Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Percentage.
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.
Ratios
Percentage
Numbers
But try the problem first...
Answer: is 252.
AIME I, 2008, Question 1
Elementary Number Theory by David Burton
First hint
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
Second Hint
here given that \(\frac{3k}{5k+20}\)=\(\frac{58}{100}\) then k=116
Final Step
then 2k+20=252.
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