Skip to main content

2007 AMC 12B Problem 10

Problem 10 of 25EasierArithmeticProblem-Solving Techniques

Some boys and girls are having a car wash to raise money for a class trip to China. Initially 40%40\% of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then 30%30\% of the group are girls. How many girls were initially in the group?

Answer choices

Show solution

Solution

Since two girls leave while two boys arrive, the total group size is unchanged. The drop from 40%40\% to 30%30\% girls corresponds to the two girls who left. So those two girls are 10%10\% of the group, meaning the group has 2020 people. The initial number of girls was 40%40\% of 20,20, or 8.8. Thus, the correct answer is C.
AoPS wiki

Tagged: percentage · invariant

More practice