Posted by **Astrid** on Sunday, January 6, 2008 at 10:38pm.

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.

- 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

x-y = -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 x-y=-2

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

## Answer This Question

## Related Questions

- math ALGEBRA - When the digits of two-digits numbers are reversed, the new ...
- algebra - The sum of the digits of a two-digit number is eleven. If the digits ...
- algebra - A number consists of two digits. The sum of twice the tens digit an 5 ...
- algebra - The value of a certain two-digit number is eight times he sum of its ...
- Algebra 2 - The sum of the digits of a two-digit number is 9. If the digits are ...
- Algebra 1 - The sum of the digit of a two digit number is 13. If the digits are ...
- Modeling with Linear Systems - The digits of a two-digit number sum to 8. When ...
- Algebra 1 - Hello, can someone check my answer the the question below? When the ...
- math - the sum of the digits of a two digit number is 9. if the digits are ...
- math - The sum of the digits of a two-digit number is 16. If the digits are ...

More Related Questions