SOLUTION: In a fraction twice the numerator in 2 more than the denominator. If 3 is added to the numerator and to the denominator the new fraction is 2/3. Find original fraction.

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Question 979209: In a fraction twice the numerator in 2 more than the denominator. If 3 is added to the numerator and to the denominator the new fraction is 2/3. Find original fraction.
Answer by subhash Sharma (1) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the numerator and y= the denominator Now we are told that
2x=y+2----------equation (1)
and (x+3)/(y+3)=2/3
3(x+3)=2(y+3)
3x+9=2y+6
3x-2y=-3------------equation (2)
Solve from eqn. (1) and (2) we get,
2x-y=2----------(1)×2
3x-2y=-3--------(2)×1
Now eqn.(1)-(2) we get,
4x-2y=4
3x-2y=-3
X=7
And from equation(1) y=12
Therefore, original fraction x/y=7/12.