Problem:
Some boys and girls are having a car wash to raise money for a class trip to China. Initially of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then of the group are girls. How many girls were initially in the group?
Answer Choices:
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Solution:
Let be the number of girls and the number of boys initially in the group. Then . After two girls leave and two boys arrive, the size of the entire group is unchanged, so . The solution of the system of equations
is and , so there were initially 8 girls.
OR
After two girls leave and two boys arrive, the size of the group is unchanged. So the two girls who left represent of the group. Thus the size of the group is 20 , and the original number of girls was of 20 , or .
The problems on this page are the property of the MAA's American Mathematics Competitions