Question

Alex is 12 years older than George.

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.

Answer 1

George : Carl : Alex = 1 : 12 : 4

Explanation:

let a = Alex's age in years

let g = George's age in years

let c = Carl's age in years

Given:

• Alex is 12 years older than George

⇒ a = 12 + g

⇒ g = a - 12

Given:

• Carl is three times older than Alex

⇒ c = 3a

Given:

• The sum of their ages is 68

⇒ a + g + c = 68

Substitute the first two equations in the last equation and solve for a:

⇒ a + (a - 12) + 3a = 68

⇒ 5a - 12 = 68

⇒ 5a = 80

⇒ a = 16

Substitute the found value of a into the other equations to find g and c:

⇒ g = 16 - 12 = 4

⇒ c = 3(16) = 48

Therefore:

• Alex = 16 years old
• George = 4 years old
• Carl = 48 years old

Ratio

George : Carl : Alex = 4 : 48 : 16

Reduce by dividing by 4 → 1 : 12 : 4