SOLUTION: One positive integer is 5 more than the other. When the reciprocal of the larger number is subtracted from the reciprocal of the smaller, the result is 5/14. Find the two integers.

Algebra ->  Rational-functions -> SOLUTION: One positive integer is 5 more than the other. When the reciprocal of the larger number is subtracted from the reciprocal of the smaller, the result is 5/14. Find the two integers.      Log On


   

Question 878194: One positive integer is 5 more than the other. When the reciprocal of the larger number is subtracted from the reciprocal of the smaller, the result is 5/14. Find the two integers. My answers are 2 and -7 but I am being told you cannot have a negative number. If so, why?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I think you thought the two values for the smaller 
were the two answers, and so you didn't find the larger.
You should have discarded the -7 and kept the 2, then
added 5 to the 2 to get +7.

When the reciprocal of the larger number is subtracted 
from the reciprocal of the smaller, the result is 5/14

Let x = smaller
Larger = x+5  

The equation is:

1%2Fx-1%2F%28x%2B5%29%22%22=%22%225%2F14

Multiply through by 14x(x+5)

 14(x+5) - 14x = 5x(x+5)

14x + 70 - 14x = 5x2 + 25x

            70 = 5x2 + 25x

             0 = 5x2 + 25x - 70

Divide through by 5:

           
             0 = x2 + 5x - 14

             0 = (x + 7)(x - 2)

                 x + 7 = 0;   x - 2 = 0
                     x = -7;      x = 2  <--you mistakenly thought these
                                            were the two answers.

But we must discard the -7 because it is negative.  Then add 5
to the 2 to get the larger.

x = smaller = 2
Larger = x+5 = 2+5 = 7

Edwin