Question

1. In a certain fraction, the denominator is 4 less than
the numerator. If 3 is added to both the numerator
9
and denominator, the resulting fraction is -. Find the
7​

Answer 1

Answer:

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Answer 2

Question :-

• In a certain fraction, the denominator is 4 less than the numerator. If 3 is added to both the numerator and denominator, the resulting fraction is 9/7. Find the fraction.

Answer :-

• The fraction is 18/14.

To find :-

• The fraction.

Solution :-

Let the numerator be "x".

Then :-

• The denominator will be "x - 4", as it is 4 less than the numerator.

Now, adding 3 to both the numerator and denominator :-

• The numerator will be "x + 3".
• The denominator will be "x - 4 + 3".

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$\longmapsto\sf\dfrac{x + 3}{x - 4 + 3} = \dfrac{9}{7}$

$\longmapsto\sf x - 4 + 3 \: (9) = 7 \: (x + 3)$

$\longmapsto\sf9x - 36 + 27 = 7x + 21$

$\longmapsto\sf9x - 9 = 7x + 21$

$\longmapsto\sf9x = 7x + 21 + 9$

$\longmapsto\sf9x = 7x + 30$

$\longmapsto\sf9x - 7x = 30$

$\longmapsto\sf2x = 30$

$\longmapsto\sf x = \dfrac{30}{2}$

$\longmapsto\underline{ \boxed{\sf x = 15}}$

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Hence, the numerator and the denominator of the fraction are as follows :-

$\rm Numerator = x + 3 = 15 + 3 = 18.$

$\rm Denominator = x - 4 + 3 = 15 - 4 + 3 = 14.$

Thus :-

• The fraction is 18/14.