SOLUTION: The numerator of a certain fraction is 4 times the denominator. If 6 is added to both the numerator and denominator, the resulting fraction is equivalent to 2. What was the origina

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The numerator of a certain fraction is 4 times the denominator. If 6 is added to both the numerator and denominator, the resulting fraction is equivalent to 2. What was the origina      Log On


   

Question 758532: The numerator of a certain fraction is 4 times the denominator. If 6 is added to both the numerator and denominator, the resulting fraction is equivalent to 2. What was the original fraction?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the denominator.
Then, the numerator is 4x, and the fraction is 4x%2Fx, which is equivalent to 4.
4x%2Fx=2
If you add 6 to both the numerator and the denominator, the resulting fraction is
%284x%2B6%29%2F%28x%2B6%29=2
Multiplying both sides of the equal sign times %28x%2B6%29 we get
%28%284x%2B6%29%2F%28x%2B6%29%29%2A%28x%2B6%29=2%2A%28x%2B6%29
4x%2B6=2%28x%2B6%29
4x%2B6=2x%2B12
4x-2x=12-6
2x=6
x=3.......denominator
4x=4%2A3=12......numerator
so, fraction is 12%2F3

if 6 is added to both the numerator and denominator, we have
%2812%2B6%29%2F%283%2B6%29=18%2F8=2