SOLUTION: The sum of the digits of a two digit number is 9. If 9 is added to the number, then the digits are reversed.Find the number.

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Question 893067: The sum of the digits of a two digit number is 9. If 9 is added to the number, then the digits are reversed.Find the number.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
t = tens digit
u = units (ones) digit
10t+u = the number
10u+t = the number with the digits reversed

The sum of the digits of a two digit number is 9. 
        t+u = 9

If 9 is added to the number, then the digits are reversed.
  10t+u + 9 = 10u+t

So the system of equations is

       system%28t%2Bu+=+9%2C10t%2Bu%2B9+=+10u%2Bt%29

Solve the first equation for for t

        t+u = 9
          t = 9-u

Substitute (9-u) for t in the second equation of the system:

    10t+u+9 = 10u+t
10(9-u)+u+9 = 10u+(9-u)
 90-10u+u+9 = 10u+9-u
      99-9u = 9u+9
         90 = 18u
          5 = u

Substitut 5 for u in

          t = 9-u
          t = 9-5
          t = 4

The number is 45.

Checking: We add 9 to 45 and get 54, which is the number
with the digits reversed.

Edwin

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be XY.  Then when you add 9 you have this:

                     XY
                    + 9
                   ----
                     YX

9 is so large that when you add 9 to Y you are bound to have to carry 1.  
So let's put a 1 to carry above the X in the left column:

                     1
                     XY
                    + 9
                   ----
                     YX

 The 1 to carry shows that Y is 1 more than X, so do a little trial and error:

Is X 1 and Y 2?  No because 1+2 isn't 9.

                     1
                     12
                    + 9
                   ----
                     21

But the digits are reversed.

Is X 2 and Y 3?  No because 2+3 isn't 9.

                     1
                     23
                    + 9
                   ----
                     32

But the digits are reversed.

Is X 3 and Y 4?  No because 3+4 isn't 9.

                     1
                     34
                    + 9
                   ----
                     43

But the digits are reversed.

Is X 4 and Y 5?  4+5=9.  HEY! RIGHT

                     1
                     45
                    + 9
                   ----
                     54

And the digits are reversed. HEY!  THAT'S IT!!!!

Phil