Question

The denominator of a fraction is 7 more thanbthe numerator.If 3 is added to the numerator and 2 to the denominator we get 2/3.Find the original fraction.

Answer 1

let numerator be x and denominator be x+7

ATQ

x+3/x+7+2=2/3

x+3/x+9=2/3

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

3x+9=2x+18

3x-2x=18-9

x=9=numerator

x+7=16=denominator

original fraction=9/16

Answer 2

$hi \\ here \: is \: the \: solution \\ \\ let \: the \: denominator \: be \: 7 + x \\ and \: numerator \: be \: x \\ \\ so \\ \ \frac{x + 3}{7 + x + 3} = \frac{2}{3} \\ \\ (x + 3)3 = (7 + x)2 \\ \\ 3x + 9 = 14 + 2x \\ \\ 3x - 2x = 14 - 9 \\ \\ x = 5 \\ so \: the \: fraction \: is \: \frac{8}{12} \\ \\ \\ verify \\ \frac{5 + 3}{5 + 7} = \frac{2}{3}$