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Question

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?

Accepted Answer

Let the two digits be a and b. Then, 5a + 5b = 10a + b - 10b - a = 9a - 9b, or 2a = 7b. This yields a = 7 and b = 2 because a, b < 10. Then, 72 + 27 = 99.