SOLUTION: The denominator of a certain fraction is three more than twice the numerator. If 7 are added to both terms of the fraction, the resulting fraction is 3/5. Find the original fractio

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The denominator of a certain fraction is three more than twice the numerator. If 7 are added to both terms of the fraction, the resulting fraction is 3/5. Find the original fractio      Log On


   

Question 89773: The denominator of a certain fraction is three more than twice the numerator. If 7 are added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
The denominator of a certain fraction is three more than twice the numerator. If 7 are added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.
%28x%2Fy%29 = C
%28x%2F%282x%2B3%29%29=C
%28%28x%2B7%29%2F%28%283x%2B2%29%2B7%29%29=3%2F5%29 [original fraction]
or
%28%28x%2B7%29%2F%28%283x%2B9%29%29%29=3%2F5%29
.
(5)(x+7)=(3)(3x+9) [cross-multiply to simplfy]
.
5x+35=9x+27 [solve for the x-term]
35=9x-5x+27
35=4x+27
35-27=4x
8=4x
x=2
.
check by plugging (x=2) back into the original equation
%28%28x%2B7%29%2F%28%283x%2B2%29%2B7%29%29=3%2F5%29
%28%282%2B7%29%2F%28%283%282%29%2B2%29%2B7%29%29=3%2F5%29
%289%2F15%29 = 3%2F5%29 [reducing]
%283%2F5%29 = 3%2F5%29 [checks out]