Question

When we add 6 to the numerator of a fraction, we get 1/2.whwn we add 7 to the denominator of the same fraction .we get 1/3.fing the fraction by forming two equations​

Answer 1

Answer:

The required fraction is 19/50

Step-by-step explanation:

Given :

When we add 6 to the numerator of a fraction, we get 1/2.

When we add 7 to the denominator of the same fraction, we get 1/3.

To find :

the fraction

Solution :

Let the numerator be x and the denominator be y.

$\longmapsto \sf Fraction=\dfrac{Numerator}{Denominator}$

So, the fraction is x/y.

• 6 is added to numerator of the fraction.

New numerator = x + 6

New fraction =  $\tt \dfrac{x+6}{y}$

According to the question :

$\sf \dfrac{x+6}{y}=\dfrac{1}{2} \\\\ \sf 2(x+6)=1 \times y \\\\ \sf 2x+12=y \\\\ \boxed{\sf 2x-y=-12} \ \ \longrightarrow eqn.1$

• 7 is added to the denominator of the fraction.

New denominator = y + 7

New fraction =  $\tt \dfrac{x}{y+7}$

According to the question :

$\sf \dfrac{x}{y+7}=\dfrac{1}{3} \\\\ \sf 3(x)=1(y+7) \\\\ \sf 3x=y+7 \\\\ \boxed{\sf 3x-y=7} \ \ \longrightarrow eqn.2$

Subtract eqn. 1 from eqn. 2 :

3x - y - (2x - y) = 7 - (-12)

3x - y - 2x + y = 7 + 12

 x = 19

Substitute x = 19 in eqn. 2 ,

3x - y = 7

3(19) - y = 7

 57 - y = 7

  y = 57 - 7

  y = 50

Therefore,

$\frak{\pmb{\sf The \ original \ fraction=\dfrac{19}{50} }}$