SOLUTION: The numerator of a fraction is 4 less than its denominator. If you add 1 to both the numerator and the denominator, the resulting fraction is equal to 2/3. What is the original f

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The numerator of a fraction is 4 less than its denominator. If you add 1 to both the numerator and the denominator, the resulting fraction is equal to 2/3. What is the original f      Log On


   

Question 685076: The numerator of a fraction is 4 less than its denominator. If you add 1 to both the numerator and the denominator, the resulting fraction is equal to 2/3. What is the original fraction?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The numerator of a fraction is 4 less than its denominator. If you add 1 to both the numerator and the denominator, the resulting fraction is equal to 2/3. What is the original fraction?

Let the denominator = x


Then the numerator is 4 less than that: x-4


If you add 1 to the denominator you have: x+1


If you add one to the numerator you have: x-4+1 or x-3

So your algebraic equation is:
%28x-3%29%2F%28x%2B1%29=2%2F3
Cross Multiply:
3%28x-3%29=2%28x%2B1%29
3x-9=2x%2B2
3x-2x-9=2x-2x%2B2
x-9=2
x-9%2B9=2%2B9
x=11
Your denominator is x=11
Your numerator is: x-4=11-4=7
The original fraction is: highlight%287%2F11%29

Do a sanity check...if you add 1 to the numerator and denominator, does it indeed reduce to 2/3's?

Happy Calculating!