A man is 6 years older than his spouse.
Four years ago he had been married to her exactly half of his life and 10 years from now she will have been married to him for two thirds of her life.
What will be the man's age on their 50th anniversary (provided they both survive)?

The key variables are an age (his or hers) and age at marriage (his or hers.)
I chose x for her age and x+6 for his age and x-m for her age at marriage (ie they were married m years ago.

Four years ago he had been married to her exactly half of his life becomes (1/2)(x+2) = x+6-m

10 years from now she will have been married to him for two thirds of her life becomes (1/3)(x+10) = x-m

from the first x-m = (1/2)x - 5
from the second x-m = (1/3)x + (10/3)

(1/2)x - 5 = (1/3)x + (10/3)
(1/6)x = (10/3)+5
x = 20+30=50
m=30

On their 50th anniversary the man will be x+6-m+50 = 76 years old.

Posted by Jer on 2011-05-23 14:56:32