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17 December, 04:02

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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Answers (1)
  1. 17 December, 04:14
    0
    It's 53.

    Step-by-step explanation:

    Let the number be xy so the digits are x and y, so:

    x + y = 8 ... (1)

    Reversing the 2 digits we have the number 10y + x and this equals

    10x + y - 18 so we have the equation:-

    10x + y - 18 = 10y + x

    9x - 9y = 18

    x - y = 2 ... (2) Adding equations (1) and (2) we have:

    2x = 10

    x = 5

    and y = 8 - 5 = 3.

    So the original number is 53.

    We can check this as follows

    Original number is 53 so the reverse is 35.

    53 - 35 = 18 which checks out.
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