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The sum of the digits of a two digit number is multiplied by 8. The result is 8 more than the 2-digit number. Find the
number

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  1. If the digits are a and b,

    8(a+b) = 8+10a+b
    8a+8b = 8+10a+b
    7b - 2a = 8

    The number is 32

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  2. How it comes 32

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  3. from the above
    7b - 2a = 8
    2a = 7b-8
    a = (7b-8)/2

    but a and b can only be a numbers between 0 and 9
    and since 7b-8 is divided by 2, the expression
    7b-8 must be even.
    This means that b must be an even number

    let's try values of b

    let b=2
    a = (14-8)/2 = 3
    giving us 32

    let b=4
    a = (28-8)/2 = 10 , but that is too large, and will only get larger if we pick higher values of b

    so all done, the number is 32

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