Problem:
The difference between a two-digit number and the number obtained by reversing its digits is 5 times the sum of the digits of either number. What is the sum of the two-digit number and its reverse?
Answer Choices:
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Solution:
Let be the larger number. Then , which simplifies to . The only nonzero digits that satisfy this equation are and . Therefore the larger number is 72 , and the required sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions