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Algebra Difficulty 3.8 AMC 10/12 Find the answer Slovenia

For non-zero real numbers aa, bb and cc we have
a=b+2c,a+c=b+d,b=d+c. 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=a2cb = a - 2c and d=bc=a3cd = b - c = a - 3c, we have a+c=a2c+a3ca + c = a - 2c + a - 3c and a=6ca = 6c.

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