In a dance school with 35 students, a poll shows 12 are studying tap dance and 19 are studying ballet. What is the minimum number of students in the school who are studying both tap and ballet?

Question

anonymous · Answer

$$
12+19-35 
$$Or something like that.

openstudier · Answer

But, the answer is 0.

openstudier · Answer

I got 4, but apparently it's 0.

anonymous · Answer

12+19 = 31  clearly there does not need to be any overflow.

openstudier · Answer

I don't understand though... is it because 31<35?

agent0smith · Answer

^yes, there may not be anyone in the middle portion of the venn diagram. There could be other dances being studied that weren't mentioned. That should be U = 35 in my diagram btw... the universal set = 35 members.

(12-x) + x + (19-x) + y = 35

y being students not in either ballet/tap.

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openstudier · Answer

Oh, I understand. Thank you!