SOLUTION: 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

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.
RELATED QUESTIONS
In a class of 40 students, 17 have ridden an airplane; 28 have ridden a boat; 10 have... (answered by richwmiller,dkppathak)

QUESTION TIME!~ in a class of 40 students, 17 have ridden an airplane 28 have ridden a (answered by psbhowmick)

In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat, 10 have... (answered by richwmiller)

In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat, 10 have... (answered by Edwin McCravy)

Suppose that 47% of all Americans have flown in an airplane at least once and that 28% of (answered by stanbon)

there are 40 students. 17 students rode an airplane only, 28students rode boat only,... (answered by richwmiller)

Amy is riding on a bike course that is 40 miles long. So far, she has ridden 12 miles of... (answered by ikleyn)

A boy rides a bike 8 miles. The trip would have taken 20 minutes less if he had ridden 2... (answered by nerdybill,stanbon,mangopeeler07)

A cyclist covers 30km at a uniform speed. If he had ridden 5km/h faster, he would have... (answered by josgarithmetic,ikleyn)