2015 AMC 8 Problem 24

A baseball league consists of two four-team divisions. Each team plays every other team in its division N games. Each team plays every team in the other division M games with N>2M and M>4. Each team plays a 76-game schedule. How many games does a team play within its own division?

\textbf{(A) } 36 \qquad \textbf{(B) } 48 \qquad \textbf{(C) } 54 \qquad \textbf{(D) } 60 \qquad \textbf{(E) } 72

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