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.
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.
Other useful links
- https://www.cheenta.com/cubes-and-rectangles-math-olympiad-hanoi-2018/
- https://www.youtube.com/watch?v=ST58GTF95t4&t=140s
Related Program
AMC – AIME Boot Camp… for brilliant students.
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