2000 CEMC Pascal Problems/Problem 12

Problem

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

$\text{ (A) }\ 50 \qquad\text{ (B) }\ 70 \qquad\text{ (C) }\ 80 \qquad\text{ (D) }\ 100 \qquad\text{ (E) }\ 200$

We can find $a$ using this fact:

$2(10 + a) = 30$

$a + 10 = \frac{30}{2} = 15$

$a = 5$

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We can now use this to find $b$ :

$b = 2(5 + 30) = 2 \times 35 = 70$

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Finding $c$ , we get:

$c = 2(30 + 70) = 2 \times 100 = \boxed {\textbf {(E) } 200}$

~anabel.disher