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How many three-digit numbers are increased by 99 when their digits are reversed?

Question

How many three-digit numbers are increased by 99 when their digits are reversed?

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Solution

Sure, let's solve this step by step:

  1. A three-digit number is in the form of 100a + 10b + c, where a, b, and c are the digits of the number.

  2. When the digits are reversed, the number becomes 100c + 10b + a.

  3. According to the problem, the reversed number is 99 more than the original number. So, we can set up the equation: 100c + 10b + a = 100a + 10b + c + 99.

  4. Simplifying this equation, we get 99c - 99a = 99, or a - c = 1.

  5. Since a and c are digits, the only possible values for them are a = 1, c = 0; a = 2, c

This problem has been solved

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