Question

The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted from both,
its numerator and denominator, the fraction becomes 2/3. Find the original fraction.​

Answer 1

Answer:

✅Here's your answer

✔Let the numerator be x and denominator be y=x+9

According to question....

$\frac{x}{</strong><strong>x</strong><strong> + 9} \\ \\ if \: 7 \: \: is \: subtracted \: from \: both \: side \\ \\ \frac{x - 7}{x + 9 - 7} = \frac{2}{3} \\ \\ \frac{x - 7}{x + 2} = \frac{2}{3}$

$3(x - 7) = 2(x+ 2) \\ \\ 3x - 21 = 2x + 4 \\ \\ 3x - 2x = 4 + 21 \\ \\ x = 25$

So the numerator is 25..and denominator is y= 25+9= 34

✔ Fraction is 25/34...

Hope it helps ✌✌...

Answer 2

Answer:

Step-by-step explanation:

Let x=numerator,

y=denominator.

y=x+7 - - - - - (i)

(x+3)/(y+3) = 2/3

(Cross multiply)

3(x+3)=2(y+3)

3x+9=2y+6

(subtract 9 from both sides)

3x+9–9=2y+6–9

3x=2y+6–9

3x=2y-3 - - - - - - - (ii)

(substitute the value of equation (i) into (ii))

3x=2(x+7)-3

3x=2x+14–3

3x=2x+11

(subtract 2x from both sides)

3x-2x=2x+11–2x

x=11.

(substitute the value of x into equation (i))

y=7+11

y=18.

so numerator =11,

denominator = 18.

So original fraction is 11/18.

3/11th of original fraction is

= 11/18 x 3/11

= (11x3)/(18x11)

= 3/18

=1/6.