+743 Find the average of all the integer values of $M$ such that $\frac{M}{56}$ is strictly between $\frac{1}{5}$ and $\frac{5}{4}$.
+129845 1/5 < M/56 < 5/4
1/5 < M /56 M/56 < 5/4
56/5 < M M < 56 * 5 / 4
11.2 < M M < 70
The integer values range from 12 to 69 inclusive
The average of these = sum of the terms / number of terms
Number of terms = 69 -12 + 1 = 58
Sum = (12 + 69) * (58/2) = 2349
Average = 2349 / 58 = 40.5
