Question

the sum of the numerator and denominator of a fraction is 14 if 2 is added to numerator and 2 is subtracted from denominator it becomes 5/3 find the fraction​

Answer 1

The fraction is (6.75/7.25).

Step-by-step explanation:

We are given that the sum of the numerator and denominator of a fraction is 14. If 2 is added to numerator and 2 is subtracted from denominator it becomes 5/3.

Let the original fraction be $\frac{x}{y}$  where numerator = $x$ and denominator = $y$ .

We are given with the following conditions;

• First condition states that the sum of the numerator and denominator of a fraction is 14, that means;

                                $x+y=14$

                                 $x=14-y$    ------------ [Equation 1]

• Second condition states that if 2 is added to numerator and 2 is subtracted from denominator it becomes 5/3, that means;

                                 $\frac{x+2}{y-2}=\frac{5}{3}$

                          $3(x+2) =5(y-2)$

                             $3x+6 =5y-10$

                             $3(14-y)+6 =5y-10$         {using equation 1}

                             $42-3y+6 =5y-10$

                              $48-3y =5y-10$

                                 $5y+3y =48+10$

                                  $8y=58$

                                   $y=\frac{58}{8}=7.25$

Now, putting value of y in equation 1, we get;

                         $x=14-7.25$

                            = 6.75

Therefore, the original fraction is $\frac{x}{y} =\frac{6.75}{7.25}$ .