My son is seven times older than my grandson and I am 12 times older than my grandson. If you add all our ages together, the sum is 100 years. Can you tell me my age in years?

Question

My son is seven times older than my grandson and I am 12 times older than my grandson. If you add all our ages together, the sum is 100 years. Can you tell me my age in years?

Answer 1

Let S = son's age

Let G = grandson's age

Let Y = your age

7G = S (you son's age is 7x your grandson's age)

12G = Y (your age is 12x your grandson's age)

12G + 7G + G = 100 yrs (all ages added together is 100 yrs)

Solving the last for G you have 20G = 100 and G = 5 yrs old (grandson's age)

Son's age = 7G = 7x5 = 35 years old

Your age = 12G = 12x5 = 60 years old