1988 AHSME Problem 25

X, Y and Z are pairwise disjoint sets of people. The average ages of people in the sets X, Y, Z, X \cup Y, X \cup Z and Y \cup Z are 37, 23, 41, 29, 39.5 and 33 respectively. Find the average age of the people in set X \cup Y \cup Z.

\textbf{(A)}\ 33\qquad \textbf{(B)}\ 33.5\qquad \textbf{(C)}\ 33.6\overline{6}\qquad \textbf{(D)}\ 33.83\overline{3}\qquad \textbf{(E)}\ 34

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