algebra word problem

Question

The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. Find the original number.

Answer 1

Any two digit positive integer can be written as                                                 10(ten's digit) + one's digit.  For example, 87 = 10(8) + 7.              

 

Let x = ten's digit of the number and y = one's digit of the number.

 

So,  the number = 10x + y 

      the number with the digits reversed = 10y + x

 

Then we get the following system of equations:

 

     x + y = 8  

   (10y + x) = (10x + y) + 18

 

So, x + y = 8

    9x - 9y = -18

 

Divide the second equation by 9 to get:  x + y = 8

                                                                            x - y  = -2

 

Add the equations to obtain 2x = 6

 

Therefore, x = 3 and y = 5

 

So, the number in question is 35