Question

Please help me. Set theory word problems that are complicated for me. :(

In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat, 10 have ridden a train, 12 have ridden both an airplane and a boat. 3 have ridden a train only and 4 have ridden an airplane only. Some students in the class have not ridden any of the three modes of transportation and an equa number have taken all three.
a. How many students have used all three modes of transpo?
b.How many students have taken only the boat?

Answer 1

Diagrams help. Start by making a Venn diagram with three overlapping circles.

Answer 2

Now, it might be easiest to label the regions where only one form of transportation was used. So, the number of people who only used airplanes, only used trains, and only used boats could be added to the diagram.

Answer 3

I forgot to add that there were students who used none of the three, and they would be represented by the area outside of the three circles.

Answer 4

Does that make sense so far?

Answer 5

The number of people who took no transportation is equal to the number of people who used all three. Since they don't tell you what that number is, you can use x.

Answer 6

yeahp. it's making sense. :)..im following. im figuring it out too.

Answer 7

Ok, good :)

Answer 8

So, then, since they tell you that 12 people have ridden both an airplane and a boat, what label would you put here?

Answer 9

If you are working on this and figuring out the rest of the labels, please let me know, and I won't bother you while you are trying to work! :)

Answer 10

the question mark is 12 (between airplane and boat)

Answer 11

no go on i'll brainstorm as you go. truth is im really confused with the problem.