The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number

Discussion in 'Calculator Requests' started by math_celebrity, Jan 8, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number?


    Let x and (16-x) represent the original ten and units digits respectively

    Reversing its digits increases the number by 18

    Set up the relational equation
    [10x + (16-x)] + 18 = 10(16 - x) + x

    Solving for x
    9x + 34 = 160 - 9x

    Combine like terms
    18x = 126

    Divide each side of the equation by 18
    18x/18 = 126/18
    x = 7

    So 16 - x = 16 - 7 = 9
    The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up.
    The number in our answer is 79
     

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