Categories
AIME I Algebra Arithmetic Math Olympiad USA Math Olympiad

Percentage Problem | AIME I, 2008 | Question 1

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.

Subscribe to Cheenta at Youtube