ExplanationBy rearranging the first two equations, you obtain c = 7 – ab and b = 5 − ac.

By substituting these relationships into the third equation, a + (5 − ac) + (7 − ab) = 6 is obtained.

Manipulating the equation yields a − ac − ab + 12 = 6, or a − a (c + b) + 6 = 0. Since a + b + c = 6, b + c = 6 − a.

Substituting this into the previous equation yields \(a - a (6 - a) + 6 = a - 6a + a^2 + 6 = 0\), or \(a^2 - 5a + 6 = 0\).

Factoring and finding the roots gives you a = 2 or a = 3.

If a = 2—by substituting the value back into the equations—then b = 2 and c = 1. If a = 3, then b = 3 and c = 1. You are looking for abc, and either way, the value is 3 × 2 × 1 = 6. The answer is choice (B).

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Sandy

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