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)   (Show Source): You can put this solution on YOUR website!
Let's say that your original fraction is . And we know that , so we can re-write the original fraction as .

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

which we are told is equal to , so

. This is an equation in a single variable that can be solved by ordinary methods.

Step 1: Cross-multiply.


Step 2: Distribute the 2 on the left


Step 3: Add -3p to both sides


Step 4: Add -2 to both sides


Step 5: Collect like terms:


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

If the numerator of the original fraction is 3, the denominator is , hence the original fraction must have been

Check:


Hope this helps,
John
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