SOLUTION: The denominator of a positive common fraction is 3 more than its numerator. If 5/28 is added to this fraction, the result is the same as the positive difference between the recipr
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Question 753794: The denominator of a positive common fraction is 3 more than its numerator. If 5/28 is added to this fraction, the result is the same as the positive difference between the reciprocal of the original fraction and 1. What is the common fraction?
Here is the equation I come up with but I have stalled...
(x/x+3)+ 5/28 = (x+3/x)-1
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Let d = denominator
Let n = numerator.
First sentence means, , so the common fraction is .
IF , THEN . We want to find or solve for n.
The positive value of the difference is part of what we want to use, so let's just write the value in its expected positive form:
which we could simplify
What should be done with that? Back to the whole second sentence and the symbolic meaning of IF,THEN...
You should expect better results continueing from that equation, so the rest is being left for you to try (but be sure to understand the path to the last highlighted equation first).
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
The denominator of a positive common fraction is 3 more than its numerator. If 5/28 is added to this fraction, the result is the same as the positive difference between the reciprocal of the original fraction and 1. What is the common fraction?
Here is the equation I come up with but I have stalled...
(x/x+3)+ 5/28 = (x+3/x)-1
Let numerator be N
Then denominator is N + 3
(You’re correct up to this point)
28N(N) + 5N(N + 3) = 28(N + 3)(N + 3) – 1(28N)(N + 3) ----- Multiplying by LCD, 28(N)(N + 3)
11N(N - 4) + 21(N - 4) = 0
(N - 4)(11N + 21) = 0
N – 4 = 0 or 11N + 21 = 0
N, or numerator = 4 OR 11N = - 21 (ignore)
Since N or numerator = 4, then denominator = 4 + 3, or 7
Common fraction is:
You can do the check!!
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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