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If the digits of the number are reversed, the number is increased by 36. The sum of the digits in the number is two and one–half times their difference. What is the number?

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  1. let the unit digit be y
    let the tens digit by x

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

    10y + x = 10x + y - 36
    9y - 9x = -36
    x - y = 4

    10x+y - (10y+x) = 36
    9x - 9y = 36 ----> x - y = 4
    x = 4+y

    x+y = 2.5(x-y)
    2x + 2y = 5(x-y)
    2x + 2y = 5x - 5y
    7y = 3x
    (7/3)y = x

    so (7/3)y = 4+y
    7y = 12 + 3y
    4y = 12
    y = 3

    if y = 3 , x = 7
    the original number is 73

    check:
    number reversed is 73
    73-37 =36 , that's good

    sum of digits = 7+3 = 10
    2.5(7-3) = 2.5(4) = 10

    my answer is correct

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  2. Where did the 9y - 9x =36 came though?

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