SOLUTION: the denominator of a certain fraction is three times the numerator. if 1 is added to the numerator and subtracted from the denominator, the result equals 1/2. find the original fra

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Question 119283: the denominator of a certain fraction is three times the numerator. if 1 is added to the numerator and subtracted from the denominator, the result equals 1/2. find the original fraction.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that your original fraction is p%2Fq. And we know that q=3p, so we can re-write the original fraction as p%2F3p.

If we add 1 to the numerator and subtract 1 from the denominator, we get:

%28p%2B1%29%2F%283p-1%29 which we are told is equal to 1%2F2, so

%28p%2B1%29%2F%283p-1%29=1%2F2. This is an equation in a single variable that can be solved by ordinary methods.

Step 1: Cross-multiply.
2%28p%2B1%29=%283p-1%29

Step 2: Distribute the 2 on the left
2p%2B2=3p-1

Step 3: Add -3p to both sides
2p-3p%2B2=-1

Step 4: Add -2 to both sides
2p-3p=-1-2

Step 5: Collect like terms:
-p=-3

Step 6: Multiply both sides by -1
p=3, giving us the numerator of the original fraction.

If the numerator of the original fraction is 3, the denominator is 3%2A3=9, hence the original fraction must have been 3%2F9

Check:
%283%2B1%29%2F%289-1%29=4%2F8=1%2F2

Hope this helps,
John