# Math Help - word problem

1. ## word 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.

2. Originally Posted by Panaboy
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.
Let n = numerator
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