Question

the numerator of a fraction is 7 less than the denominator if 3 is added to the numerator and 9 is subtracted from the denominator the new fraction is equal to 3 upon 2 find the original fraction​

Answer 1

Given:

The numerator of a fraction is 7 less than the denominator if 3 is added to the numerator and 9 is subtracted from the denominator the new fraction is equal to 3 upon 2

To find:

The original fraction​

Solution:

Let,

"x" represents the numerator

"y" represents the denominator

The numerator of a fraction is 7 less than the denominator

i.e., $x = y - 7$ Equation1

As per the question, we get

$\frac{x \:+ \:3}{y\: -\: 9} = \frac{3}{2}$

$\implies 2(x + 3) = 3(y - 9)$

$\implies 2x + 6 = 3y - 27$

substituting from equation1

$\implies 2(y - 7) + 6 = 3y - 27$

$\implies 2y - 14 + 6 = 3y - 27$

$\implies 2y - 8 = 3y - 27$

$\implies 3y - 2y = 27 - 8$

$\implies \bold{y = 19}$

∴ $\bold{x} = y -7 = 19 - 7 = \bold{12}$

Thus, the original fraction is → $\boxed{\bold{\underline{ \frac{12}{19} }}}$.

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