SOLUTION: The ratio of the numerator to the denominator of a fraction is three to five. If fifteen is subtracted from the numerator and added to the denominator, the new fraction reduces to

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the numerator to the denominator of a fraction is three to five. If fifteen is subtracted from the numerator and added to the denominator, the new fraction reduces to       Log On


   

Question 1068148: The ratio of the numerator to the denominator of a fraction is three to five. If fifteen is subtracted from the numerator and added to the denominator, the new fraction reduces to one-third. Find the original fraction.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
x%2Fy+=+3%2F5+ (1)
+%28x-15%29%2F%28y%2B15%29+=+1%2F3+ (2)
(1) —> +x+=+%283%2F5%29y+ (1')
Substitute this into (2) so you'll have one equation with one unknown (y):
+%28%283%2F5%29y+-+15%29%2F%28y%2B15%29+=+1%2F3+
+%283%2F5%29y+-+15+=+%281%2F3%29%28y%2B15%29+
etc.
Solve for y then plug into (1), (1') (easiest), or (2) to get x.