SOLUTION: The numerator of a fraction is 1 more than the denominator. If 1 is added to the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4. Find the or

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Question 825543: The numerator of a fraction is 1 more than the denominator. If 1 is added to the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4. Find the original fraction
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the original numerator and d = the original denominator. Then the numerator with 1 added to it would be: n + 1.

With two variables we need two equations to solve this problem. "The numerator of a fraction is 1 more than the denominator." translates into:
n = d + 1
and "If 1 is added to the numerator, and the denominator is unchanged, the resulting fraction has a value of 3/4" translates into:
%28n%2B1%29%2Fd+=+3%2F4

Now we can solve. Since the first equation is already solved for n, the Substitution Method seems like it would be easiest. Substituting for n in the second equation we get:
%28%28d%2B1%29%2B1%29%2Fd+=+3%2F4
Simplifying we get:
%28d%2B2%29%2Fd+=+3%2F4
Cross-multiplying we get:
%28d%2B2%29%2A4+=+d%2A3
which simplifies to:
4d%2B8+=+3d
Subtracting 4d we get:
8+=+-d
Multiplying (or dividing) both sides by -1 we get:
-8+=+d

Now we find the value for n. Using the first equation, n = d + 1, and the value we found for d, we should get n = -7. And since n and d are the original fraction:
%28-7%29%2F%28-8%29