For three numbers p, q and r: $\frac{p+q}{2} + r = 39$, $\frac{q+r}{2} + p = 35$ and $\frac{p+r}{2} + q = 34$. What is the average of p, q and r?

Explanation

1. 01

   Add the three equations. Each number appears in two of the fractions (worth ½ + ½) and once on its own, so it is counted 2 times in all.

2. 02

   So the left side totals $2(p + q + r) = 39 + 35 + 34 = 108$.

3. 03

   $p + q + r = 54$, so the average = $\frac{54}{3} = 18$.