Let p be $x$ more than the average, and q be $x$ less than the average.

Then: $p = k + x$ $q = k - x$

We know the average of p, q, and r is k: $\frac{(p + q + r)}{3} = k$

Substitute the values of p and q: $\frac{[(k + x) + (k - x) + r]}{3} = k$ $\frac{(2k + r)}{3} = k$ $2k + r = 3k$ $r = k$

Hence, the value of r is k.