Problem:
Of the students attending a school party, of the students are girls, and of the students like to dance. After these students are joined by more boy students, all of whom like to dance, the party is now girls. How many students now at the party like to dance?
Solution:
Suppose at the beginning there are students at the party. Then students are girls, and students like to dance. When the boys join the party, there are girls at the party, which must equal the original number of girls at the party. Thus , which implies , and . Thus the current number of students who like to dance is .
The problems on this page are the property of the MAA's American Mathematics Competitions