Question

The sum of numerator and denominator of a fraction is 12. three times the numerator is one less than double the denominator. Find the fraction.​

Answer 1

Step-by-step explanation:

Let's say, Numerator is x and Denominator is y

So, x+y = 12 --- (i)

& 3x = 2y-1

Or, 3x-2y = -1 --- (ii)

(i)×2 + (ii)×1,

2x+2y = 24

3x-2y = -1

-----------------

5x = 23

$x = \frac{23}{5}$

Putting the value of x in (i),

$\frac{23}{5} + y = 24 \\ y = 24 \: - \frac{23}{5} \\ y = \frac{97}{5}$

$fraction \: = \frac{x}{y} \\ = \frac{ \frac{23}{5} }{ \frac{97}{5} } \\ = \frac{23}{97}$