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# Percentage Problem | AIME I, 2008 | Question 1

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Percentage. you may use sequential hints.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Percentage.

## Percentage Problem – AIME I, 2008

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.

• is 107
• is 252
• is 840
• cannot be determined from the given information

### Key Concepts

Ratios

Percentage

Numbers

AIME I, 2008, Question 1

Elementary Number Theory by David Burton

## Try with Hints

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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