Well, 11 is clearly the correct answer. He didn't get to the answer the same way I did but his way seems to work. To test his method just plug in different numbers to the same problem.
For example, I picked random numbers and did the same problem with 50 trays, 42 with plates, 21 with cups. Using my method, you get 13 with cups and plates. Take his method and cups are 42% and plates are 84% which is 126. 26/100=13/50. Really a pretty clever little method.
The only thing I'd say is that this method gets a little messier if you have numbers that aren't quickly and easily converted to percentages. Notice my numbers as well as the original ones lend themselves to his method pretty well. If there were 33 total trays with 27 having plates and 15 having cups, I'd find his method much less convenient than a more standard approach.
