# math

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A poll was taken of 100 students at a commuter campus to find out how they got to campus. The results are below. How many are not using any of the three?
35 said they drove alone.
35 rode in a carpool.
30 rode public transportation.
3 used both carpools and public transportation.
6 used both a carpool and sometimes their own cars.
6 used buses as well as their own cars.
1 used all three methods.
______students

• math -

The total number of answers recorded is

35+35+30 = 100

3 of these answers belong to 1 person:

At this point in the problem,

person count = 1
answer count = 100-3 - 97

6 used buses as well as their own cars. One of these persons would be the person who used all three; so 5 used ONLY buses and cars

person count = 1 + 5 = 6
answer count = 97 - 5*2 = 97 - 10 = 87

6 used both a carpool and sometimes their own cars. One of these persons would have been the person who used all three methods; so 5 used ONLY a carpool and sometimes their own cars.

person count = 6 + 5 = 11
answer count = 87 - 5*2 = 87-10 = 77

3 used both carpools and public transportation; Of these, 1 of these also uses their own car; 2 use ONLY carpools and public transportation

person count = 11 + 2 = 13
answer count = 77 - 2*2 = 77-4 = 73

73 students only use one means of transportation
2+5+5 = 12 students use ONLY 2 means of transportation
1 student uses all three

73+12+1 = 86 students use some of the forms of transportation listed. A total of 100 students answered the questionnaire

100-86 = 14

14 students are not using any of these three

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