Why is it always 1089

I told you during Easter that I was reading two recommended crime novels. In the book "Hevnens Alkymi" (the Alchemy of Revenge), it is described a calculation which you too can use as a party game/joke:

Add two number together and always end with 1089.

Here is How:
Pick a three digit number. The three numbers used must be different. i.e. 437

Reverse that number. 437 becomes 734
Take the smallest three digit number from the largest.
734 - 437 = 297
Take the answer and reverse that number. 297 becomes 792
Add that number to the answer of the subtraction. 792 + 297 = 1089
The answer will be 1089!

So Why does it do this?

You will need a little bit of algebra.
But stick with it, it is not difficult.
Represent the number with ABC
Reverse this to get CBA
Remember that A is Hundreds B is tens and C is units

Take CBA from ABC like this
Hundreds Tens Units

A B C
minus
C B A

Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones
(-100, +90, +10 = 0, so won't change answer):

Hundreds Tens Units

A-1 B+9 C+10
minus
C B A

A-1-C 9 10+C-A
Last Step: Reverse the answer and add the two numbers together.

A-1-C 9 10+C-A
plus
10+C-A 9 A-1-C

9 18 9
(simplify:)
10 8 9

As predicted the answer was 1089

If you did not follow my explanation here, go to Math is Fun for a better presentation and other update of your math competence. Have fun!