The Aunt and Her Nephew
Aunt Annie and her nephew Neal were walking down the street. In the distance, they saw three well-dressed people disappear down an alley. Aunt Annie asked Neal if he knew how old they were. Neal did not.
The three were well-known to Aunt Annie, so she was able to give two helpful clues:
The product of the three ages is 2,450.
The sum of their ages is twice Neal’s age.
Neal was grateful, and went away to think for a few minutes. Being a clever and creative mathematician, he was able to make good use of the clues.
When Neal returned, he told his Aunt that the clues were very helpful, but they were not enough information. She agreed.
Aunt Annie added one more clue:
All three of the ages are less than hers!
Neal was delighted. He already knew how old Aunt Annie was, and he now had enough information to determine the ages of the three well-dressed people.
How old are the three?
How old is Neal?
How old is Aunt Annie?
