A number consist of 2 digits whose sum is 8, If 8 is subtracted from the number, the digits interchange their place. The number is​

Question

A number consist of 2 digits whose sum is 8, If 8 is subtracted from the number, the digits interchange their place. The number is​

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Melanie 1 week 2021-09-15T20:09:25+00:00 2 Answers 0

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    0
    2021-09-15T20:10:53+00:00

    Step-by-step explanation:

    Let’s say the two digit number is 10x + y, where x is the first digit and y is the second digit.

    The sum of the digits is 8:

    x + y = 8

    If 8 is subtracted from the number, the digits switch place.

    10x + y − 8 = 10y + x

    Simplify the second equation:

    9x − 8 = 9y

    Substitute from the first equation.

    y = 8 − x

    9x − 8 = 9 (8 − x)

    9x − 8 = 72 − 9x

    18x = 80

    x = 4.444

    There’s a problem.  x isn’t an integer.  Are you sure you copied the problem correctly?  Perhaps you meant if 18 is subtracted from the number, the digits switch place.

    9x − 18 = 9 (8 − x)

    9x − 18 = 72 − 9x

    18x = 90

    x = 5

    y = 8 − x

    y = 3

    So the number is 53.

    0
    2021-09-15T20:10:57+00:00

    x+y=8\\10x+y-8=10y+x\\\\x+y=8|\cdot9\\9x-9y=8\\\\9x+9y=72\\\underline{9x-9y=8}\\18x=80\\x=\dfrac{80}{18}=\dfrac{40}{9}

    x is not integer, so there must be a mistake in the problem.

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