Question

The sum of the numerator and denominator of a certain positive fraction is 8. if 2 is added to both the numerator and denominator, the fraction is increased by 4/35. Find the fraction

Answer 1

2/33.please tell me the answer

Answer 2

Answer:

The fraction is $\frac{3}{5}$

Step-by-step explanation:

Given : The sum of the numerator and denominator of a certain positive fraction is 8. if 2 is added to both the numerator and denominator, the fraction is increased by 4/35.

To find : The fraction?

Solution :

let the numerator be x and denominator be y.

The fraction is $\frac{x}{y}$.

Given that their sum = 8.

$x + y =8$  ------ (1)

$y=8-x$ --------- (2)

Given that if 2 is added to both numerator and denominator, the fraction is increased by $\frac{4}{35}$

According to question,

$35(x + 2)(8-x) = 35x(10-x)+4(8-x)(10-x)$

$-35x^2 +210x + 560 = -31x^2 +278x + 320$

$-35x^2 -68x +240=-31x^2$

$-4x^2 -68x + 240 = 0$

$x^2 + 17x -60=0$

$x^2 - 3x +20x - 60 = 0$

$x(x - 3) + 20(x - 3) = 0$

$x = 3 (or) x = -20.$

Neglect x=-20

So, x=3

Substitute in equation (2)

$y=8-x$

$y=8-3$

$y=5$

Therefore, The fraction is $\frac{3}{5}$