the numerator of a fraction is 7 less than the denominator. If 9 is added to both the numerator and denominator, the value of the resulting fractions is 2/3. Fi

Question

the numerator of a fraction is 7 less than the denominator. If 9 is added to both the numerator and denominator, the value of the resulting fractions is 2/3. Find the original fraction.

Answer 1

Hi Ann

 

You start with:

(x-7)/x

 

Then you add 9 to numerator and denominator and

set it equal t 2/3

 

 ( x-7)+ 9.         2

------------   = ------

   x + 9              3

 

(x+2)/(x+9) = 2/3

 

cross multiply

 

3(x+2) = 2(x+9)

 

3x + 6 = 2x + 18

 

Can you finish solving for x?

The original fraction is then (x-7)/x

 

Understand?

Answer 2

Let x = denominator 

 

Then, x -7 = numerator

 

[(x - 7 + 9 / (x + 9) = 2/3

 

(x+2) / (x+9) = 2/3

 

2(x+9) = 3(x+2)

 

2x + 18 = 3x + 6

 

         x = 12

 

The fraction is 5/12.