Question 64
Let $a$, $b$, $c$ be real numbers such that
$$
3 a b + 2 = 6 b, \quad 3 b c + 2 = 5 c, \quad 3 c a + 2 = 4 a
$$
Suppose the only possible values for the product $a b c$ are $r / s$ and $t / u$, where $r / s$ and $t / u$ are both fractions in lowest terms. Find $r+s+t+u$.
$$
3 a b + 2 = 6 b, \quad 3 b c + 2 = 5 c, \quad 3 c a + 2 = 4 a
$$
Suppose the only possible values for the product $a b c$ are $r / s$ and $t / u$, where $r / s$ and $t / u$ are both fractions in lowest terms. Find $r+s+t+u$.