Overlapping Sets - The Matrix
Out of 50 students in a 10th grade class, 20 students take AP history and 32 take AP Biology. If 12 students take neither class, how many students take both classes?

Using the diagram, also find A Only, B Only and C Only


((80 - y)/5)/3
((80 - y)/5)/3
Multiply by lcd of 15. (3*5)
First multiply by common factor of 3 to get rid of first denominator.
(80 - y)/5
Then multiply by common factor of 5 to get rid of second denominator.
80 - y
Three competing juice makers conducted a blind taste test with mall shopers. The shoppers could choose to taste any number of the three brands of juices, but had to select at least one they liked.







































