Question 10
Let $a,b,c$ be nonzero integers satisfying
$$2\left(\frac a{a'}\right)+3\left(\frac{b'}b\right)=5,$$
$$5\left(\frac b{b'}\right)+2\left(\frac{c'}c\right)=3.$$
Find $abc+a'b'c'$.
Notation clarification: the primed symbols $a',b',c'$ denote three further nonzero integers, separate from $a,b,c$; all six symbols are nonzero.
$$2\left(\frac a{a'}\right)+3\left(\frac{b'}b\right)=5,$$
$$5\left(\frac b{b'}\right)+2\left(\frac{c'}c\right)=3.$$
Find $abc+a'b'c'$.
Notation clarification: the primed symbols $a',b',c'$ denote three further nonzero integers, separate from $a,b,c$; all six symbols are nonzero.