SOLUTION: the numerator of a certain fraction is 5 times the denominator. if 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the ori

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: the numerator of a certain fraction is 5 times the denominator. if 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the ori      Log On


   

Question 656308: the numerator of a certain fraction is 5 times the denominator. if 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. what was the original fraction?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the denominator.
Then, the numerator is 5x, and the fraction is 5x%2Fx, which is equivalent to 5.
5x%2Fx=5
If you add 6 to both the numerator and the denominator, the resulting fraction is
%285x%2B6%29%2F%28x%2B6%29
That fraction is equivalent to 2, so we can write
%285x%2B6%29%2F%28x%2B6%29=2
Multiplying both sides of the equal sign times %28x%2B6%29 we get
%28%285x%2B6%29%2F%28x%2B6%29%29%2A%28x%2B6%29=2%2A%28x%2B6%29 --> 5x%2B6=2%28x%2B6%29 --> 5x%2B6=2x%2B2%2A6 --> 5x%2B6=2x%2B12
Subtracting 2x from both sides we get
5x%2B6-2x=2x%2B12-2x --> 3x%2B6=12
Subtracting 6 from both sides we get
3x%2B6-6=12-6 --> 3x=6
Dividing both sides by 3 we get
3x%2F3=6%2F3 --> x=2
So the original fraction was
5x%2Fx=5%2A2%2F2
or highlight%2810%2F2%29