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MathNet 2011 Question 14

Math Olympiad Vault · MathNet 2011

Question 14

For non-zero real numbers $a$, $b$ and $c$ we have
$$
a = b + 2c, \quad a + c = b + d, \quad b = d + c.
$$
Which of the following equalities is certainly true?
(A) $d = 2c$
(B) $a = 3c$
(C) $a = 6c$
(D) $a = b + 2d$
(E) $b = 2a + 2d$