algebra

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

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  1. 53

  2. Sum = 8 = 7+1 = 6+2 = 5+3 = 4+4
    Select 5, and 3:
    Original #: 53.
    Reversed: 35.
    Difference = 53-35 = 18.

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    posted by Henry
  3. Here is how you do this with algebra.
    Let x = 10s digit
    and y = units digit.
    So the number is 10x + y
    and you know that if you reverse the number it is 10y + x.
    The problem tells you that
    10x + y = 10y+x+18 which simplifies to
    9x-9y=18
    The second equation is x + y = 8. Solve those two equations simultaneously this way.
    9x-9y = 18
    x+y=8
    ---------
    Multiply equation 2 by 9 and you have these two equations.
    9x - 9y = 18
    9x + 9y = 72
    -------------
    add
    18x = 90
    x = 90/18 = 5 which is the 10s digit.

    Since x + y = 8, then
    5 + y = 8 and y = 8-5=3 which is the units digit so the number is 53

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