Question

Find a : b:c:d if:
a: b = 2:3
b:c= 5:2
b:d=1:2

Answer 1

`\boxed{a:b:c:d = 1: (3)/(2):(3)/(5):3}`

Explanation:

Determine all the variables in terms of a single variable, a

Ratios are nothing but fractions

`a:b = (a)/(b)`

We have

`(a)/(b) = (2)/(3)\\\\\longrightarrow b = (3)/(2)a`

`(b)/(c) = (5)/(2)\\\\\longrightarrow c = (2)/(5) b = (2)/(5)\cdot (3)/(2) a`

`c = (3)/(5)a`

`(b)/(d) = (1)/(2)`

`\longrightarrow d = 2b = 2\cdot (3)/(2)a = 3a`

So a:b:c:d becomes

`a : (3)/(2)a : (3)/(5)a : 3a`

Which is

`1: (3)/(2):(3)/(5):3`

Answer:

`\boxed{a:b:c:d = 1: (3)/(2):(3)/(5):3}`