June 2019
Problem of the Month
Family Age Problem
by Sam Loyd
A man made the following statements:
My son is five times as old as my daughter,
and my wife is five times as old as the son,
and I am twice as old as my wife,
whereas grandmother, who is as old as all of us put together,
is celebrating her eighty-first birthday today.
How old is the son?
You must show your algebra.
Solution to the Problem:
The son is five years old.
Let x = daughter's age
Then 5x = son's age
Then 25x = wife's age
Then 50x = man's age
So x + 5x + 25x + 50x = 81
81x = 81
so, x =1 and 5x = 5.