word problems

Question

The sum of the digits of a two-digit number is 10. If 18 is added to the number, the result is equal to the number obtained by reversing the digits of the original number.  Find the original number 

Answer 1

Let the two digit number be xy.  The y is is the ones place in the number and the x is in the tens place, so the value of the number is 10x + y.  Since you have two unknowns (x and y), you need two equations.

 

Equation 1.  The sum of the digits of a two-digit number is 10:

 

x + y = 10

 

Equation 2. If 18 is added to the number, the result is equal to the number obtained by reversing the digits of the original number:

 

10x + y + 18 = 10y + x

9x -9y = -18

 

Your system of two equations is:

 

x + y = 10

9x - 9y = -18

 

Can you solve it ?  (HINT: use substitution or elimination)