Vial V is 2/3 full of a certain solution and vial W, which has 50%

Hello,

Let me try helping you with this one.

It is mentioned in the question that the volume of W is 50% larger than the volume of V. Hence, W=\(\frac{3}{2}\)*V
This implies that V=\(\frac{2}{3}\)*W
Now, V is filled with 2/3 with the solution and W is filled 3/4 with the solution.
Half of the solution in V is filled into W. We need to find the fraction of W that is filled. So, we have to express everything in terms of W.

Half of the solution in V in terms of W is 1/3. When we express that in terms of W, it becomes

half the volume of solution in V=\(\frac{1}{3}\)*\(\frac{2}{3}\)*W
This is added to 3/4 of the volume W.
The total volume is (\(\frac{1}{3}\)*\(\frac{2}{3}\)*W)+(\(\frac{3}{4}\)*W)=\(\frac{35}{36}\)*W

Hence, the answer is E.

Hope this helps! Let me know if I could help you any further.