Problem:
The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let Jack's age be and Bill's age be . In five years Jack will be twice as old as Bill. Therefore
so . The expression is a multiple of 8 if and only if is a multiple of 8 . Since both and are 9 or less, the only solution is and . Thus Jack is 31 and Bill is 13 , so the difference between their ages is .
The problems on this page are the property of the MAA's American Mathematics Competitions