jmc

Question

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 13 of all the ninth graders are paired with 25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

Accepted Answer

Let the number of sixth graders be s, and the number of ninth graders be n. Thus, n3=2s5, which simplifies to n=6s5. Since we are trying to find the value of n3+2s5n+s, we can just substitute 6s5 for n into the equation. We then get a value of 6s53+2s56s5+s = 6s+6s1511s5 = 4s511s5 = 411.