SOLUTION: A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are: 64 like ateneo only 108 like

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are: 64 like ateneo only 108 like       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 622674: A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are:
64 like ateneo only
108 like ateneo and ust
190 like ust
86 like ateneo and lasalle
51 like ateneo and lasalle but not ust
164 like lasalle
42 like lasalle and ust but not ateneo
Questions:
1. how many students like ateneo?
2. how many like lasalle and ust?
3. how many like all 3 universities?
4. how many do not like lasalle?
5. how many do not like any of the 3 universities?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
A survey among 370 4th year students conducted to know in which private university do they want to apply for college. The results of the survey are:
64 like ateneo only
108 like ateneo and ust
190 like ust
86 like ateneo and lasalle
51 like ateneo and lasalle but not ust
164 like lasalle
42 like lasalle and ust but not ateneo
Questions:
1. how many students like ateneo?
number of students that like ateneo is 223
2. how many like lasalle and ust?
number of students that like lasalle and ust is 277
3. how many like all 3 universities?
number of students that like all 3 universities is 35
4. how many do not like lasalle?
number of students that do not like lasalle is 205
5. how many do not like any of the 3 universities?
number of students that do not like all 3 universities is 29
you can make a table as follows:
                                  ateneo       ust          lasalle       none
none                                                                      29
ateneo only                       64
ust only                                       40
lasalle only                                                36
ateneo and ust only               73           73
ateneo and lasalle only           51                        51
ust and lasalle only                           42           42
ateneo and ust and lasalle only   35           35           35

total                             223          190          164           29

your venn diagram would look like this:
$$$
the intersection of ateneo and lasalle is 51
the intersection of ateneo and ust is 73
the intersection of ust and lasalle is 42
the intersection of all 3 is 35
the breakdown of the analysis is as follows:
ateneo only is 64 (given)
86 like ateneo and lasalle but 51 like ateneo and lasalle only.
this means that the 86 includes students that like all 3.
strip that out and you get 35 students like all 3 (86 - 51).
108 like ateneo and ust.
strip out 35 that like all 3 and you get 73.
42 like lasalle and ust but not ateneo (given)
since 164 like lasalle and 42 like lasalle and ust only and 35 like all 3 and 51 like lasalle and ateneo only, this leaves 164 - 42 - 35 - 51 = 36 that like lasalle only.
since 190 like ust and 73 like ust and ateneo only and 35 like all 3 only 42 like ust and lasalle only, this leaves 190 - 73 - 35 - 42 = 40 tht like ust only.
that totals up to 341 that like ateneo or ust or lasalle or a combination of them.
since total students are 370, then the number of students that don't like any of them is equal to 370 - 341 = 29.