The integers $a, b$ and $c$ satisfy the equations $a+5=b$ and $5+b=c$ and $b+c=a$. The value of $b$ is
(A) -30
(B) -20
(C) -10
(D) 0
(E) 5
Since $a+5=b$, then $a=b-5$.

Since $a=b-5$ and $c=5+b$ and $b+c=a$, then

$$
\begin{aligned}
b+(5+b) & =b-5 \\
2 b+5 & =b-5 \\
b & =-10
\end{aligned}
$$

(If $b=-10$, then $a=b-5=-15$ and $c=5+b=-5$ and $b+c=(-10)+(-5)=(-15)=a$, as required.)

ANSwer: (C)