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11 June, 15:45

This is a popular type of problem that appeared in mathematics textbooks in the 1970s and 1980s. can you find the answer? the sum of the digits of a two-digit number is 6. if the digits are reversed, the difference between the new number and the original number is 18. find the original number.

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  1. 11 June, 15:56
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    A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).

    Say the mystery number is a two digit number = xy

    * that's not x times y but two side by side digits.

    Info given:

    the sum of the digits of a two-digit number is 6

    x + y = 6

    if the digits are reversed, yx the difference between the new number and the original number is 18.

    **To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10 (5) + 1 (4))

    Original number = 10x + y

    Reversed/New number = 10y + x

    Difference:

    10y + x - (10x + y) = 18

    9y - 9x = 18

    9 (y - x) = 18

    y - x = 18/9

    y - x = 2

    Now we have two equations in two variables

    y - x = 2

    x + y = 6

    Re-write one in terms of one variable for substitution.

    y = 2 + x

    sub in to the other equation to combine them.

    x + (2 + x) = 6

    2x + 2 = 6

    2x = 6 - 2

    2x = 4

    x = 2

    That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.

    2 + y = 6

    y = 4

    number "xy" = 24
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