If $z=4, x+y=7$, and $x+z=8$, what is the value of $x+y+z$ ?
(A) 9
(B) 17
(C) 11
(D) 19
(E) 13

Part B: Each correct answer is worth 6.
Solution 1

Since $z=4$ and $x+y=7$, then $x+y+z=(x+y)+z=7+4=11$.

## Solution 2

Since $z=4$ and $x+z=8$, then $x+4=8$ or $x=4$.

Since $x=4$ and $x+y=7$, then $4+y=7$ or $y=3$.

Therefore, $x+y+z=4+3+4=11$.

ANSWER: (C)