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.
{{{(x/y)}}} = C
{{{(x/(2x+3))}}}=C
{{{((x+7)/((3x+2)+7))}}}={{{3/5)}}}  [original fraction]
or
 {{{((x+7)/((3x+9)))}}}={{{3/5)}}}
.

 (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

{{{((x+7)/((3x+2)+7))}}}={{{3/5)}}}
{{{((2+7)/((3(2)+2)+7))}}}={{{3/5)}}}
{{{(9/15)}}} = {{{3/5)}}} [reducing]
{{{(3/5)}}} = {{{3/5)}}} [checks out]