math

The sum of the digits of a two-digit number is 14. If the numbers are reversed, the new number is 18 less than the original number. Find the original number.

I know Ana asked this question, but i don't understand how to get the equations.

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asked by Astrid
  1. I thought Damon did a pretty good job of explaining this question before

    Ok, here is my approach, perhaps it will make sense to you.

    Let the unit digit of the original number be x
    Let the tens digit by y
    then the original number was 10y+x

    We were told the sum of the digits is 14, so
    x+y=14, this is your first equation

    the number reversed would be 10x+y
    but this is 18 less than the original number, so....

    10x+y + 18 = 10y+x , (since it was 18 less, I added 18 to make them "equal")

    9x - 9y = -18
    x-y = -2 , this is your second equation.

    I will leave it up to you to solve them

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    posted by Reiny
  2. I don't understand how to get the second equation

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    posted by Astrid
  3. would you agree that according to my definition, the original number is 10y+x and the number reversed is 10x+y ???

    your problem stated "the new number is 18 less than the original number." which translates into

    10x+y < 10y+x by 18, so I added 18 to the "smaller" side to make them "equal", thus

    10x+y + 18 = 10y+x
    surely you can see how that simplifies to x-y=-2

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    posted by Reiny
  4. So the answer would be 86?

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    posted by Astrid
  5. Do the digits of 86 add up to 14?
    Is 68 less than 86 by 18 ??

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    posted by Reiny

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