How many students taken only the boat?

Question

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 equal number have taken all three. How many students have used all the three modes of transportation? How many students taken only the boat?

Answer 1

The solution requires a picture. Draw a large circle. This represents the number of students, 40.

Inside the big circle draw three interlocking circles representing airplane, boat and train (A, B, T).

You should be able to identify 7 regions formed by the interlocking circles. An 8th region is the area inside the big circle but outside the three others:

a. A only users (4)

b. B only users

c. T only users (3)

d. A and B users but not T

e. B and T users but not A

f. A and T users but not B

g. A, B and T users (x)

h. Not using any transport (x)

The numbers in brackets represent the known numbers of students in the various regions. Now we can put in other numbers. 

a=4; c=3;

a+b+c+d+e+f+g+h=40; b+d+e+f+g+h=40-3-4=33 (because we know a and c);

a+d+f+g=17; d+f+g=13;

b+d+e+g=28; f+h=5;

c+e+f+g=10; e+f+g=7; d-e=6;

d+g=12; so f=13-12=1; h=5-1=4;

b+d+e+g+h=32; e+g=6; c+f=4; b+d=22;

g=h=4; b+d+e=24; e=24-22=2; d=6+2=8; b=22-8=14.

We have all the values a to h. Users of all three modes is g=4. Those using the boat only is b=14.

(a,b,c,d,e,f,g,h)=(4,14,3,8,2,1,4,4)

Comments

I would agree with the previous solution and I think that the answer would be definitely 14, 14 students have used all of the kinds of transportation and 4 of them have used only one type. For sure , you may also get soem answers at ResearchPaperWritings or some other sources like https://www.lorainccc.edu/current+students/advising+and+counseling/counseling/problem+solving.htm.