8 Let $x, y$ and $z$ be non-negative numbers. Suppose $x+y=10$ and $y+z=8$. Let $S=x+z$. What is the sum of the maximum and the minimum value of $S$ ?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 26
8. Answer: (C)
$x+y+z=9+\frac{S}{2}$. So $x=1+\frac{S}{2}, y=9-\frac{S}{2}$ and $z=-1+\frac{S}{2}$. Since $x, y, z \geq 0$, we have $2 \leq S \leq 18$.