Question 1038955: Out of 40 students, 17 have ridden a n airplane, 28 have ridden a boat, 10 havevridden a train, 12 have ridden both airplane and boat, 4 have ridden an airplane only, 3 have ridden a train only. The number of students who havent ridden any modes of the three transportations is the same as the students who have ridden all three. How many haven't ridden any modes of the 3 transportations? Hiw many have ridden a boat?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let the no. of students who have ridden airplane be A, the no. of students who have ridden boat be B and that who have ridden train be C.
Also, let the no. of students who have ridden only airplane be A', the no. of students who have ridden only boat be B' and that who have ridden only train be C'.
If we call total number of students N then we have
N = A' + B' + C' + A∩B + B∩C + C∩A + A∩B∩C ________ (1)
Also, we know
A' = A - A∩B - C∩A ________ (2)
B' = B - A∩B - B∩C ________ (3)
C' = C - B∩C - C∩A ________ (4)
Substituting in the equation (1) we have
N = A + B + C - A∩B - B∩C - C∩A + A∩B∩C __________ (5)
Now let us list all the values that we have:
N = 40, A = 17, B = 28, C = 10, A∩B = 12, C' = 3, A' = 4
Substituting all these values into equation (5)
40 = 17 + 28 + 10 - 12 - (B∩C + C∩A) + A∩B∩C
40 = 17 + 28 + 10 - 12 - (C - C') + A∩B∩C [Using equation (4)]
40 = 17 + 28 + 10 - 12 - (10 - 3) + A∩B∩C
A∩B∩C = 4
Answer: The no. of students who have ridden all modes of transportation is 4. Following this example, calculate how many haven't ridden any of the 3 modes of transportations and how many have ridden a boat.
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