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podryga [215]
3 years ago
9

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
Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0

<u>Answer:</u>

The denominator of a fraction is 4 more than the numerator. The original fraction is \frac{27}{31}

<u>Solution:</u>

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 \frac{6}{7}

=>\frac{(x-3)}{((x+4)-3)}=\frac{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}}

= \frac{27}{31}

Hence the original fraction is \frac{27}{31}

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