2015 AMC 8 Problem 16

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 \tfrac{1}{3} of all the ninth graders are paired with \tfrac{2}{5} of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy?

\textbf{(A) } \frac{2}{15} \qquad \textbf{(B) } \frac{4}{11} \qquad \textbf{(C) } \frac{11}{30} \qquad \textbf{(D) } \frac{3}{8} \qquad \textbf{(E) } \frac{11}{15}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.