Plate Tray

How do you do this math problem from the SAT practice book?

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?

I know the answer, but I can’t figure out how to solve it. Please help!

Use Venn diagrams…two intersecting circles for this problem.

In the intersect of the two circles, b (for both)

In one non-intersect circle: 15 – b

In the other: 21 – b

then, (15 – b) + (21 – b) + b = 25

b = 11

Venn diagrams help to see the situation as well as set up the algebra.

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