SOLUTION: 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; 4 have

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Question 881544: 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; 4 have ridden an airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three. How many students have taken all three?

Found 2 solutions by richwmiller, dkppathak:
Answer by richwmiller(17219) (Show Source):
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"Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three"
which means the same number who have ridden all three have not ridden any of them
so they are the same number.
It must be 4 have ridden all three and 4 have ridden none of them (outside 4).

Answer by dkppathak(439) (Show Source):
You can put this solution on YOUR website!
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; 4 have ridden an airplane only. Some students in the class have not ridden any of the three modes of transportation and an equal number have taken all three. How many students have taken all three?
total candidates are 40
airplane =17 (A) boat =28 (B) train =10(C)
A intersection B=12 alone A =4
A= alone A + common in three +common in A and B +common in A and C
17=4 +X +(12-X ) + common in A and C
X=17-16 = 1 common in all three will be 1smilarly
17=4+11 +1
10 = 3 +1 +6
28 = 11+1 +6+10
tottal all in three set =35
number of students not ridden anything =5
Answer 01 students is ridden all three mode of transport and total 5 not ridden any transport