A algebra homework?

Question

Please help me!
Explain them!Why the result always is 10.00$
Choose 2 unique digits (1-9) to form an amount (in dollars and cents)less n 10.00$
Reverse the digits in this amount
Take difference between these two amounts
Now reverse the digits in the difference
Add these last two amounts together .
Now U have your answer is 10.89$
Please help me explain it!

Answer 1

Call the digits X and Y, with X greater than Y.
In cents we have 100 X + Y. The first reverse gives 100 Y + X.

Take the difference: 100 (X-Y) + (Y-X).
Note that the second term is negative, therefore we rewrite this as:
100 (X-Y-1) + 90 + (10-(X-Y))

The three digits are (X-Y-1), 9 and (10-(X-Y)).
Reverse this and we get 100 (10-(X-Y)) + 90 + (X-Y-1) in cents.

When you now add the two numbers all terms with X and Y fall out
and you are always left with 1089 cents.

Answer 2

This a just a simple math trick in which when you follw the same steps no matter what the number, you end up with 1089

Try the same with a 3 digit number { all digits should not be same }
Reverse the digits to get another number.
Find the positive difference between them.
Again reverse the digits and add it to the difference,

You always get 1089.

Answer 3

First can you explain how will this work if I choose the digits 1 and 9 to form the Dollar amount $19.91.
If I reverse the digits I get $ 19.91 and upon subtracting from the original amount I get 00.00

Answer 4

I already had my answer, 10.89$... why do I need to explain the solution? You want them to use them for your friends?

... And by the way... 10.89$ is not 10.00$, so no need to go around it, but I heard about his before and the solution will cancel out itself to arrive in its beginning.

Answer 5

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Answer 6

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