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The denominator of a fraction is 4 more than the numerator if both are decreased by 3 the simplified result is 6/7 find original fraction

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Answer:

The denominator of a fraction is 4 more than the numerator. The original fraction is
(27)/(31)

Solution:

Given that

Denominator of fraction is 4 more than the numerator.

Let’s say numerator of fraction be represented by variable x.

So denominator of a faction as it is four more that numerator will be x + 4

Also given if both decreased by three than simplified result is
(6)/(7)


=>((x-3))/(((x+4)-3))=(6)/(7)

Solving above equation for x

=> 7(x – 3 ) = 6 ( x + 1 )

=> 7x – 21 = 6x + 6

=> 7x – 6x = 6 + 21

=> x = 27

Numerator of fraction = x = 27

Denominator of fraction = x + 4 = 27 + 4 = 31


\text {required fraction}=\frac{\text {numerator}}{\text {denominator}}


= (27)/(31)

Hence the original fraction is
(27)/(31)

User Brad Dougherty
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