2000 AMC 12 Problem 13

One morning each member of Angela’s family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?

\textbf {(A)}\ 3 \qquad \textbf {(B)}\ 4 \qquad \textbf {(C)}\ 5 \qquad \textbf {(D)}\ 6 \qquad \textbf {(E)}\ 7

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