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imc

prealgebra junior

Problem

Given that a, b, and c are non-zero real numbers, define

(a, b, c) = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}

, find

(2, 12, 9)

.

(A)

4

(B)

5

(C)

6

(D)

7

Solution

(2, 12, 9) = \frac{2}{12} + \frac{12}{9} + \frac{9}{2} = \frac{1}{6} + \frac{4}{3} + \frac{9}{2} = \frac{1}{6} + \frac{8}{6} + \frac{27}{6} = \frac{36}{6} = 6

. Our answer is then

6

.

Final answer

C