Age Mystery
Number Theory
Level
3
An old man was playing with his grandson before the boy started asking about their ages.
Boy: Grandpa, what will happen to our ages 7 years from now?
Grandpa: The sum of our ages will be a perfect square.
Boy: Oh, and then what will happen 7 years after that?
Grandpa: Then the ratio of my age to yours will be a perfect square.
Boy: Really? At that time will our ages combine to become 100?
Grandpa: No, my boy, but if we add your present age to the sum of our ages in 14 years, then it will be 100.
What is the sum of their present ages?
by
Worranat Pakornrat