Question

a fraction becomes 10/ 7 if 2 is added to both numerator and denominator if however 3 is subtracted from both numerator and denominator the fraction becomes 5/2 what is the fraction

Answer 1

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Answer 2

Fraction = $\frac{8}{5}$

Step-by-step explanation:

Let the numerator be x and denominator be y

Fraction =$\frac{x}{y}$

We are given that a fraction becomes 10/ 7 if 2 is added to both numerator and denominator

So,$\frac{x+2}{y+2}=\frac{10}{7}$

7x+14=10y+20

7x-10y-6=0 ---1

We are also given that  3 is subtracted from both numerator and denominator the fraction becomes 5/2

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

2x-6=5y-15

2x-5y+9=0 ---2

Plot The lines 1 and 2 on graph

7x-10y-6=0 --- Purple line

2x-5y+9=0  --- Black line

Intersection point will give the solution

(x,y)=(8,5)

So, Fraction = $\frac{8}{5}$

#Learn more:

A fraction becomes 4/5 if 1 is added to both numerator and denominator . If however, 5 is subtracted from both numerator and denominator, the fraction becomes 2/3. Find the fraction.

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