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word problem

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in a two digit number, the sum of the digit is 8. the different between this number and the number with the digit reversed is 54, what is the number.

  • word problem -

    n m = 10 n + m

    n+m = 8

    m n = n + 10 m

    n + 10 m - (10 n + m) = 54

    -9 n + 9 m = 54
    -n + m = 6
    but
    +n + m = 8
    ---------- add
    0 +2m = 14
    m = 7
    n = 1
    so
    17

  • word problem -

    original:
    unit digit -- x
    tens digit -- 8-x
    the number: 10(8-x) + x
    the number reversed: 10x + (8-x)

    10x + 8-x - (10(8-x) + x) = 54
    10x + 8 -x - 80 + 10x - x = 54
    18x = 126
    x = 7
    unit digit = 7
    tens digit = 1

    original number 17
    number reversed 71

    or

    original number is 71
    number reversed is 17

    in both cases the difference between them is 54

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