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The sum of the digits of a two-digit number is 16. If the digits are reversed the new number will be 18 greater than the original number. Find the number.

  • math -

    By trial and error, I found that three numbers meet the first criteria: 88, 79, 97.

    Which of those numbers meets the second criteria?

  • math -

    79

  • math -

    Let A = the first digit and B + the second digit.

    Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

    Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

    Therefore, A + B = 16 and 97 - 79 = 17.

  • math -

    Sorry for the mental error. The hand was slower than the eye.

    Let A = the first digit and B + the second digit.

    Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

    Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

    Therefore, A + B = 16 and 97 - 79 = 18

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