Answers: (a) 160 beers. (b) about 70 cents.
OK, so the Carolina Panthers lost to the Green Bay Packers in the NFC Championship Game, and all the cheeseheads were thrilled to watch the Packers cream the New England Patriots in the Super Bowl. Oh, well, so my prediction failed -- the rest of the problem still works.
The first part of the problem asks you to figure out how many 12-ounce beers you can get from a standard 15-gallon keg (at least, that's Beer King's standard), ignoring the head and such.
The first thing you need to do is figure out how to convert from gallons to 12-ounce glasses. I did an example very similar to that problem at the end of Section 3.2 of Handout 1 - the only difference being that the glasses in that example were 8-ounce glasses, not 12-ounce glasses. Here is the way to convert from gallons to 12-ounce glasses:
So you can get 10 and 2/3 12-ounce glasses from one gallon of liquid. Now, Beer King kegs hold 15 gallons, so all you have to do is multiply 10 and 2/3 by 15, like:
So the answer is that you can get 160 12-ounce beers from a standard 15-gallon beer keg.
Of course, you could also have done all this in one step, like:
and once again, the answer is 160 12-ounce beers.
For the second part, all you have to do is divide the cost of the keg by the number of beers you can get from the keg. So the answer to part (b) is
So the cost per beer is about 71 cents, which is pretty cheap for Sierra Nevada, really. Of course, that's just what you would pay. You could charge a lot more