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25 May, 15:31

The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.

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  1. 25 May, 15:55
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    Equation

    Let one digit be x

    Let the other digit = y

    x + y = 16

    Let the original number = 10x + y

    Let the reverse number = 10y + x

    10x + y - 18 = 10y + x

    Comment

    Bring the letters to the left and the number 18 to the right.

    10x - x + y - 10y = 18 Combine like terms.

    9x - 9y = 18 Divide both sides by 9

    x - y = 2

    Set up a set of equations and add.

    x + y = 16

    x - y = 2 Now add

    2x = 18 Divide by 2

    x = 18/2

    x = 9

    x + y = 16

    9 + y = 16 Subtract 9 from both sides.

    y = 16 - 9

    y = 7

    Check

    Original number = 97

    Reversed number 79

    Difference 18 and it checks.
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