Question

Bill is twice as old as Adam

Charlie is 3 years younger than Bill
The sum of their three ages is 27
Find the ratio of Adam's age to Charlie's age, giving your answer in the form 1:n

Answer 1

`(1)/(1.5)`

Explanation:

Let B represent Bill age

A be adam age

C be charlie age

We know that

`b = 2a`

We also know that

`c = b - 3`

And we know that

`a + b + c = 27`

Fist let subsitue c for b-3

`a + b + (b - 3) = 27`

`a + 2b - 3 = 27`

`a + 2b = 30`

We know that b=2a so

`a + 2(2a) = 30`

`a + 4a = 30`

`5a = 30`

`a = 6`

Plug that in first equation to solve for b

`b = 2(6)`

`b = 12`

Finally plug that in the final equation to solve for c.

`6 + 12 + c = 27`

`c = 9`

Know we want the ratio of Adam age, a to Charlie age, c.

So we have

`(6)/(9) = (2)/(3) = (1)/(1.5)`