The sum of the digits of a two-digit number is 11. If 45 is added to the number, the result is the number with the digits reversed. What is the equation?

Question

I know that the answer is 38 but i dont know the equation.

Answer 1

A two digit positive integer can be written as 10x+y, where x is the ten's digit and y is the one's digit.  

 

For example, 52 = 10(5)+2

 

So, if we let x = ten's digit and y = one's digit, then:

 

            x+y=11

           (10x+y)+45 = 10y+x

 

Simplify to get x+y = 11

                    9x-9y = -45

 

Dividing the second equation by 9, we have x+y = 11

                                                             x -y = -5

 

Add the equations to obtain 2x = 6.  So, x = 3

 

Since x+y=11 and x=3, y = 8.

 

The number is 38.