For some very mathy people, functions, formulas, and processes aren't the right way to understand the thinking. You have to understand the mental (likely visual) model that leads to that approach. That's one of the flaws I see with the inflexibility of classic math instruction particularly for kids who are further out there.
In this problem, if you see each quantity as a stick. You start with three sticks of the same length and clip off parts of two of them to represent the subsets (cups and plates), then you stack those sticks together and compare to the whole (trays). Clip off the part that expands past the base value and that is your overlap.
That model favors his approach. And percentages are a great generalization that allow answering many more questions about the problem set. If he answers it that quickly, then he probably has a solid mental model and the percent calculation is likely close cognitively free for him.
