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

Answer 1

Fred,

 

Let x = age of the grandson, y = age of the son, and z = age of grandfather

 

Then, the son is 7 times older than the grandson:

 

(1) y = 7x

 

The grandfather is 12 times older than the grandson:

 

(2) z = 12x

 

All three ages sum to 100:

 

(3) x + y + z = 100

 

Now substitute the values of y and z in (1) and (2) for y and z in (3);

 

x + 7x + 12x = 100

 

20x = 100

 

x = 5 (age of the grandson)

 

Grandfather's age:

 

12(5) = 60 years

 

Hope this helps!