Question

If a:b = 3:5 and a:c = 5:7, what is the value of b:c?

Answer 1

`a:b=3:5\to(a)/(b)=(3)/(5)\\\\a:c=5:7\to(a)/(c)=(5)/(7)\\\\(a)/(c):(a)/(b)=(a)/(c)\cdot(b)/(a)=(b)/(c)\\\\therefore\ (b)/(c)=(5)/(7):(3)/(5)=(5)/(7)\cdot(5)/(3)=(25)/(21)\\\\Answer:\boxed{(b)/(c)=(25)/(21)\to a:c=25:21}`