SOLUTION: The numerator of a fraction is 10 less than the denominator. If 4 is added to each, the value of the resulting fraction is 3/5. Find the original fraction. I've tried using multip

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The numerator of a fraction is 10 less than the denominator. If 4 is added to each, the value of the resulting fraction is 3/5. Find the original fraction. I've tried using multip      Log On


   

Question 7089: The numerator of a fraction is 10 less than the denominator. If 4 is added to each, the value of the resulting fraction is 3/5. Find the original fraction.
I've tried using multiples of 3/5 and subtracting 4 from the numerator and denominator hoping it will give me a solution where the numerator is 10 less than the denominator but I want a faster way of figuring this problemo ut just in case I ever get it on a test.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You could use this approach:
Let d = the denominator.
%28%28d-10%29%2B4%29%2F%28d%2B4%29+=+3%2F5 Simplify then cross-multiply.
%28d-6%29%2F%28d%2B4%29+=+3%2F5
5%28d-6%29+=+3%28d%2B4%29 Simplify and solve for d.
5d-30+=+3d%2B12 Subtract 3d from both sides.
2d-30+=+12 Add 30 to both sides.
2d+=+42 Divide both sides by 2.
d = 21
The original fraction is:
%28d-10%29%2Fd or
%2821-10%29%2F21
11%2F21 This is the original fraction.
Check:
Adding 4 to the numerator and to the denominator, we get:
%2811%2B4%29%2F%2821%2B4%29+=+15%2F25+=+3%2F5