The hog's head pub decide to make mixture thst is 50% butterbeer. how much of an 80% butterbeer solution should mixed with 20 gallon of 20% butterbeer solution to create the new mixture?

There are 20 gallons of 20% butterbeer solution.
Assume there are x gallons of 80% solution.

So total amount of the solution will be (x+20) gallons
The final solution is 50%.

So, we can set up the equation as:

.

Thus, there will be 20 gallons of 80% butterbeer solution that is needed to be mixed with 20 gallons of 20% butterbeer solution.