In a class, 22 students have been on a plane, 28 on a train, 23 on a boat, 15 on a plane and train, 20 on a train and boat, 14 on a plane and boat, 12 on all three, and 1 on none of them. how many students are in the class?

37 students are in the class

Step-by-step explanation:

There are 8 regions which the most inclusive clue is the inner one with 12.

"14 on a plane and boat" so we fill the intersection with plane and boat with 14-12=2"20 on train an boat" 20-12=8 in the intersection"15 on plane and train" = 15-12 = 3

now we look at this:

"22 students have been on a plane" 22 - (2+12+3) = 5 on the plane"28 on a train" 28 - (12+8+3) = 5 on the train"23 on a boat" 23-(12+8+2) = 1 on the boat

Just add up all the 8 numbers in the regions:

12+2+8+3+5+5+1+1=37

Hmmm i had this before , give me a sec