The denominator of a fraction is 3 less than twice the numerator.If the numerator were doubled and the denominator increased by 8, the resulting fraction would be 2/3.Find the original fraction.

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- Dec 10th 2005, 07:44 AMPanaboyword problem
The denominator of a fraction is 3 less than twice the numerator.If the numerator were doubled and the denominator increased by 8, the resulting fraction would be 2/3.Find the original fraction.

- Dec 10th 2005, 10:22 AMticbolQuote:

Originally Posted by**Panaboy**

And d = denominator

d = 2n -3 ------(i)

2n / (d+8) = 2/3 -------(ii)

Substitute the d from (i) into (ii),

2n / (2n-3 +8) = 2/3

2n / (2n +5) = 2/3

Cross multiply,

2n(3) = (2n +5)(2)

6n = 4n +10

6n -4n = 10

2n = 10

n = 10/2 = 5 --------***

So,

d = 2n-3 = 2(5) -3 = 7 ------***

Therefore, the original fraction was 5/7. ------answer.

Check,

2n/(d+8) =2/3

2(5) / (7 +8) =? 2/3

10/15 =? 2/3

2/3 =? 2/3

Yes, so, OK