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


But try the problem first…

Answer: is 252.

Source
Suggested Reading

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.

Subscribe to Cheenta at Youtube