Posted by Astrid on Sunday, January 6, 2008 at 10:38pm.
The sum of the digits of a twodigit 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.

math  Reiny, Sunday, January 6, 2008 at 11:01pm
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
xy = 2 , this is your second equation.
I will leave it up to you to solve them

math  Astrid, Sunday, January 6, 2008 at 11:31pm
I don't understand how to get the second equation

math  Reiny, Monday, January 7, 2008 at 12:04am
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 xy=2

math  Astrid, Monday, January 7, 2008 at 12:09am
So the answer would be 86?
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