AMC 8 1986 Problem 11

If $\text{A}*\text{B}$ means $\frac{\text{A}+\text{B}}{2}$, then $(3*5)*8$ is $\text{(A)}\ 6 \text{(B)}\ 8 \text{(C)}\ 12 \text{(D)}\ 16 \text{(E)}\ 30$