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.

Algebra.Com
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)   (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

       

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)   (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
RELATED QUESTIONS

The sum of two digits of a two digit number is 15. If 9 is added to it, the digits are... (answered by richwmiller,Boreal,htmentor)
a number consists of two digits whose sum is 9.if 9 is added to the number ,its... (answered by checkley79)
A two digit number is 4 times the sum of its digits. If 27 is added to that number its... (answered by josmiceli)
the sum of the digits of two digit number is 9.if the digits are reversed the new number... (answered by Maths68)
The sum of digits of a two digit numbers is 9 and if 9 is added to the number the digits (answered by ikleyn)
The sum of the two digits of a two-digit number is 6. When 18 is added to the number... (answered by Edwin McCravy)
number of two digit exceeds 4 times the sum of the digits by 3 if 36 is added to the... (answered by ptfile)
The sum of the digits of a two-digit number is 11. If 27 is added to the number, the... (answered by checkley75)
URGENT HELP: The sum of the digits of a two-digit number is 9. If the digits are... (answered by fcabanski)