Problem:
In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If of all the ninth graders are paired with of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?
Answer Choices:
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Solution:
out of every sixth graders are paired with a ninth grade buddy, and out of every ninth graders are paired with a sixth grade buddy. (The ratios are now expressed so that the number of sixth graders matches the number of ninth graders.) So out of every students are in the mentoring program. The fraction is .
Suppose that sixth graders are paired with ninth graders. Then the total number of sixth graders is , the total number of ninth graders is , and the total number of sixth and ninth graders is . There are students in the mentoring program, which is of the total number of students.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions