Grandfather age at his death

Question

Grandfather lived to a ripe old age. After he had lived 1/3 of his life he married Grandmother four years later their first daughter was born. Mother lived only 1/2 of grandmother total years grandfather lived another ten years after mothers death before he died. What was grandfather's age at his death

Answer 1

We're looking for grandfather's age at death.  We'll call it A.

 

He married grandmother after 1/3 of his life.  That would be A/3 years.

Their first daughter was born 4 years later.  That would be at A/3 + 4.

 

I'm assuming that mother is that first daughter.

From there, you've either left something out or you meant that mother lived half as long as grandfather instead of grandmother.

There's no information that will let us relate mother's age to grandfather, and nothing that would let us relate grandmother's age back to grandfather.

 

Assuming that mother lived to half of grandfather's age, that would be A/2.

Mother died A/3 + 4 + A/2.  The time of her birth plus half of grandfather's age.

Grandfather lived 10 more years. That would be A/3 + 4 + A/2 + 10.

 

Since this sum is grandfather's age (A) at death, we can set it equal to A:

A =  A/3 + 4 + A/2 + 10

A = (5/6)*A +14

A - (5/6)A = 14

(1/6)A = 14

A = 84

 

Check:

1/3 of grandfather's age = 84/3 = 28     Marriage

plus 4 years = 28 + 4 = 32                   Mom's birth

plus half of grandfather's age = 32 + 84/2 = 32 + 42 = 74      Mom's death

plus 10 more years =  74 + 10 = 84       Grandfather's death

 

Sounds reasonable.  I think that's the answer you were looking for.