Answer :
Ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4
Solution:
Let "a" be the age of Alex
Let "g" be the age of George
Let "c" be the age of Carl
Alex is 12 years older than George
Therefore,
Age of Alex = 12 + Age of George
a = 12 + g
g = a - 12 ---- eqn 1
Carl is Three times older than Alex
Age of Carl = 3 x Age of Alex
c = 3a -------- eqn 2
The sum of their ages is 68
age of Alex + age of George + age of Carl = 68
a + g + c = 68 ----------- eqn 3
Substitute eqn 1 and eqn 2 in eqn 3
a + a - 12 + 3a = 68
5a - 12 = 68
5a = 12 + 68
5a = 80
a = 16
Substitute a = 16 in eqn 2
c = 3(16) = 48
c = 48
Substitute a = 16 in eqn 1
g = 16 - 12 = 4
g = 4
Find the ratio of George’s age to Carl’s age to Alex’s age
Ratio of George’s age to Carl’s age to Alex’s age = g : c : a
g : c : a = 4 : 48 : 16
Divide the above ratio by 4 to reduce to lowest terms
g : c : a - 1 : 12 : 4
Thus ratio of George’s age to Carl’s age to Alex’s age is 1 : 12 : 4