Question

Given that a:b = 4 : 5 and a : c = 3 : 4,find the ratio of 5b : 3c

Answer 1

5b: 3c = 25 : 16

Explanation:

`(a)/(b) = (4)/(5) \: and \: (a)/(c) = (3)/(4)`

dividing both to get a : c

`(a)/(b) * (c)/(a) = (4)/(5) * (4)/(3) \\ (c)/(b) = (16)/(15) \\`

inverting the fractions

`(b)/(c) = (15)/(16)`

multiplying the numerator by 5 and denominator by 3

`(5b)/(3c) = (5 * 15)/(3 * 16) \\ = (75)/(48) \\ = (25)/(16)`

therefore,

5b: 3c = 25 : 16