Question

Alexis12yearsolderthanGeorge.

Carl is three times older than Alex
The sum of their ages is 68
Find the ratio of George’s age to Carl’s age to Alex’s age.
1:2:5:5:7


Answer 1

1:12:4

Explanation:

We let the youngest, George, age be x

From the question Alex is 12 years older than George.

This implies that,in terms of x, Alex's age is x+12

Also,Carl is three times older than Alex

This implies that, in terms of x Carl's age is 3(x+12)

The sum of their ages is 68

This implies that

`x + x + 12 + 3(x + 12) = 68`

we simplify to get the value for x

`\implies 2x + 12 + 3x + 36 = 68`

`\implies 5x + 48= 68`

subtracting 48 from both sides

`\implies 5x + 48 - 48= 68 - 48`

`\implies 5x = 20`

Dividing through by 5

`\implies (5x)/(5)= (20)/(5)`

`\implies x = 4`

Hence George is 4yrs old,Alex is 16 yrs old and Carl is 48 yrs old.

Therefore the ratio of George’s age to Carl’s age to Alex’s age is 4:48:16=1:12:4