Maths

In a two digit number the digit in the unit place is 6 less than twice the digit in the tenth place. When tha digits are reversed th number increases by 9. Find the number

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  1. let the tenth digit be x
    then the unit digit is 2x-6

    the number is 10x + (2x-6)
    the number reversed is 10(2x-6) + x
    10(2x-6) + x - (10x + (2x-6)) = 9
    20x - 60 + x - 10x - 2x + 6 = 9
    9x = 63
    x=7
    then 2x-6 = 8
    then number is 78

    check:
    87-78 = 9 , looks good

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  2. u = 2t - 6

    10u + t = 10t + u + 9

    substituting
    ... 20t - 60 + t = 10t + 2t - 6 + 9

    solve for t, then substitute back to find u

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