AMC 12 2000 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?

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