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Slovenia — National Math Olympiad

Algebra Difficulty 3.8 AMC 10/12 Find the answer Slovenia

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?

Pick one

Solution

Since $b = a - 2c$ and $d = b - c = a - 3c$ , we have $a + c = a - 2c + a - 3c$ and $a = 6c$ .

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