In the diagram, each of the five boxes is to contain a number. Each number in a shaded box must be the average of the number in the box to the left of it and

| 8 |  |  | 26 | $x$ |
| :--- | :--- | :--- | :--- | :--- |

the number in the box to the right of it. What is the value of $x$ ?
(A) 28
(B) 30
(C) 31
(D) 32
(E) 34
We label the numbers in the empty boxes as $y$ and $z$, so the numbers in the boxes are thus $8, y, z, 26, x$.

Since the average of $z$ and $x$ is 26 , then $x+z=2(26)=52$ or $z=52-x$.

We rewrite the list as $8, y, 52-x, 26, x$.

Since the average of 26 and $y$ is $52-x$, then $26+y=2(52-x)$ or $y=104-26-2 x=78-2 x$.

We rewrite the list as $8,78-2 x, 52-x, 26, x$.

Since the average of 8 and $52-x$ is $78-2 x$, then

$$
\begin{aligned}
8+(52-x) & =2(78-2 x) \\
60-x & =156-4 x \\
3 x & =96 \\
x & =32
\end{aligned}
$$

Therefore, $x=32$.

ANSWER: (D)