2000 AMC 8 Problem 23

There is a list of seven numbers. The average of the first four numbers is 5, and the average of the last four numbers is 8. If the average of all seven numbers is 6\frac{4}{7}, then the number common to both sets of four numbers is

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

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