Question

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

$4$

$6$

$8$

$10$

$12$

Answer: C

Concepts:percentage linear equation

Difficulty rating: 1330

Small Hint:

The group size does not change when two leave and two arrive

Big Hint:

The two departing girls represent $40\%-30\%$ of the group

Solution:

Two girls leave and two boys arrive, so the group size is unchanged. The two girls who left therefore represent $40\%-30\%=10\%$ of the group.

Thus the group has $2\div 0.10=20$ people, and the original number of girls was $40\%$ of $20,$ or $8.$

Thus, the correct answer is C.

2007 AMC 10B Problem 14

Answer: C

Difficulty rating: 1330

Small Hint:

Big Hint:

Solution:

Problem 14 in Other Years