Fractional equations

Question

Two numbers differ by 14. If the larger number is divided by the smaller, the quotent is 3 and the remainder is 2. Find the numbers.

Answer 1

Let x = larger number

      y = smaller number

 

Then, x - y = 14

           x/y = 3 + 2/y  

 

The second equation comes from the fact that:

     dividend/divisor = quotient + remainder/divisor

 

Multiplying the second equation by y, we get :  x - y = 14

                                                                                  x = 3y + 2

 

Substitute for x in the first equation:  (3y + 2) - y = 14

                                                                                  2y = 12

                                                                                    y = 6

So, since y = 6, x - 6 = 14

Therefore, x = 20

 

The numbers are 20, 6