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A number consists of two digits whose sum is 9. if three times the number is equal to eight times the number formed by interchanging the digits. find the number

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  1. let the unit digit be x
    and the tens digit be y
    so x+y = 9 ---> y = 9-x

    the number is 10y+x
    the number reversed is 10x + y

    3(10y+x) = 8(10x + y)
    30y + 3x = 80x + 8y
    22y = 77x
    2y = 7x
    2(9-x) = 7x
    18 - 2x = 7x
    18=9x
    x=2
    y=7

    the number is 72

    check:
    number is 72
    reverse is 27
    is 3(72) = 8(27) ? , YES

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