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

## Check the Answer

Answer: is 252.

AIME I, 2008, Question 1

Elementary Number Theory by David Burton

## Try with Hints

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.

## Other useful links

- https://www.cheenta.com/cubes-and-rectangles-math-olympiad-hanoi-2018/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s