There are 25 trays on a table in the cafeteria. Each tray contains a cup only, a plate only, or both a cup and a plate. If 15 of the trays contain cups and 21 of the trays contain plates, how many contain both a cup and a plate?

Question

I assume Venn diagrams/methods are used, but I'm not sure how to handle the intersection of the two in equation form.

Answer 1

21+15 = 36
There are only 25 trays, so 11 must contain both cup and plate.

Now you can draw the Venn diagram to see that the intersection of the two regions must contain 11.