How many did not ride on any of the three modes of transportation?

Question

In a group of 120 student, 68 had ridden a bus , 78 had ridden the LRT , 33 had ridden a jeep, while 40 had ridden both the bus and the LRT , 20 had ridden the bus and jeep , 19 had ridden the LRT and the Jeep and 15 had ridden the bus , the LRT and the Jeep.

Answer 1

Let the letters A-H represent the following sets:

A Those that did not use any of the transportation modes

B Bus users only

C LRT users only

D Jeep users only

E Bus and jeep users--not LRT users

F LRT and jeep users--not bus users

G Bus and LRT users--not jeep users

H Bus, LRT and jeep users

Now we can write equations from the given figures:

A+B+C+D+E+F+G+H=120 (all students)

B+E+G+H=68 (bus users)

C+F+G+H=78 (LRT users)

D+E+F+H=33 (jeep users)

G+H=40 (bus and LRT users)

E+H=20 (bus and jeep users)

F+H=19 (LRT and jeep users)

H=15 (bus, LRT and jeep users)

F=19-H=4, E=20-H=5, G=40-H=25

D=33-(E+F+H)=33-(5+19)=33-24=9

C=78-(F+G+H)=78-(4+40)=78-44=34

B=68-(E+G+H)=68-(5+40)=68-45=23

A=120-(B+E+G+H + C+D+F)=120-(68+34+9+4)=120-115=5

So 5 students didn't use any of the transportation.