In the diagram, every number beginning at 30 equals twice the sum of the two numbers to its immediate left. The value

| 10 | $a$ | 30 | $b$ | $c$ |
| :--- | :--- | :--- | :--- | :--- |

of $c$ is
(A) 50
(D) 100
(B) 70
(E) 200
(C) 80
In the diagram, every number beginning at 30 equals twice the sum of the two numbers to its immediate left. The value of $c$ is
(A) 50
(B) 70
(C) 80
(D) 100
(E) 200

## Solution

If we start the question by working with the first three boxes, we have:

$$
\begin{aligned}
30 & =2(10+a) \\
\text { or, } \quad 15 & =a+10 \\
a & =5
\end{aligned}
$$

If $a=5$ then $b=2(30+5)=70$ and, in turn, $c=2(70+30)=200$.

ANSWER: (E)