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:

Step-by-step explanation:

Let the numerator=x

Then as per the given condition denominator=x+9

Now, if we subtract 7 from numertator then it will be x-7

             and on subtracting 7 from denomiator x+9-7=x+2

Fraction will be (x-7/x+2)=2/3

                          $\frac{x-7}{x+2}$=$\frac{2}{3}$

                          3(x-7)=2(x+2)

                          3x-21=2x+4

                           x=25

Answer 2

Answer:

Let the numerator - x

& the denominator - y

ATQ

$\mathcal{y - x = 9} -- \orange{(1)} \\ \frac{x -7 }{y - 7} = \frac{2}{3} \\ \implies 3x - 21 = 2y - 14 \\ \implies 3x - 2y = 7 - - \orange{(2)}$

Now ...

here we need To find the value of x and y from (1) and (2)

It is now clearly visible that we can apply Substitution Method here to make out the values of x and y

$\therefore \: from \: \orange{(1)} \: we \: get \\ x = \pink{y - 9} - - \orange{(3)} \\ from \: \orange{(3)} \: and \: \orange{(2)} \: we \: get$

$3( \pink{y - 9}) - 2y = 7 \\ 3y - 27 - 2y = 7 \\ y = \blue{34} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ substituting \: this \: value \: in \: \orange{(3)} \: we \: get \\ x \: = 34 - 9 \\ \implies \: x = \red{25}$

Therefore the the fraction we came to find is

$\huge{ \frac{x}{y} = \frac{25}{34} } \\ \huge\orange{\mathbf{verification}} \\ it \: can \: be \: verified \: with \: two \: steps \\ \large step \: 1 \: \\ denominator - numerator \: = 9 \\ \implies 34 - 25 = 9 \\ \\ \large{step \: 2} \\ \frac{numerator - 7}{denominator - 7} = \frac{25 - 7}{34 - 7} = \frac{18}{27} \\ = \pink{\frac{2}{3} } \\ thus \: verified$

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