jmc

Let $S$ be the sum of the 10 numbers. Then the average of the 10 numbers is $\frac{S}{10}$, so $\frac{S}{10}=85$, or $S=850$. After 70 and 76 are removed, the sum of the remaining 8 numbers is $S-70-76=850-70-76=704$. So the average of the remaining 8 numbers is $\frac{704}{8}=\boxed{88}$.