SOLUTION: can someone help me ,please and thank yu! the denominator of a certain fraction is six times the numerator. if 3 is added to the numerator and subtracted from the denominator, t

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Question 469305: can someone help me ,please and thank yu!
the denominator of a certain fraction is six times the numerator. if 3 is added to the numerator and subtracted from the denominator, the resulting fraction is equivalent to 2/5. find the original fraction.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = numerator and y = denominator


"the denominator of a certain fraction is six times the numerator." means that y+=+6x


"if 3 is added to the numerator and subtracted from the denominator, the resulting fraction is equivalent to 2/5" means that %28x%2B3%29%2F%28y-3%29=2%2F5


%28x%2B3%29%2F%28y-3%29=2%2F5 Start with the second equation.


%28x%2B3%29%2F%286x-3%29=2%2F5 Plug in y=6x


5%28x%2B3%29=2%286x-3%29 Cross multiply


5x%2B15=12x-6 Distribute.


5x=12x-6-15 Subtract 15 from both sides.


5x-12x=-6-15 Subtract 12x from both sides.


-7x=-6-15 Combine like terms on the left side.


-7x=-21 Combine like terms on the right side.


x=%28-21%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=3 Reduce.


y=6x Go back to the first equation.


y=6%283%29 Plug in x=3


y=18 Multiply


So the original fraction is 3%2F18