Three numbers are such that if the average of any two of them is added to the third number, the sums obtained are 164, 158 and 132 respectively. What is the average of the original three numbers?

$$\eqalign{ & \frac{{a + b}}{2} + c = 164 \cr & \frac{{b + c}}{2} + a = 158 \cr & \frac{{c + a}}{2} + b = 132 \cr & \overline {\frac{{2\left( {a + b + c} \right)}}{2} + a + b + c = 454} \cr & a + b + c = 227 \cr & {\text{Average}} = \frac{{a + b + c}}{3} = \frac{{227}}{3} = 75\frac{2}{3} \cr} $$