Survey Problem. Am I doing this correctly?

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gardenia

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Am I solving this problem correctly?

A survey was taken to determine where students study. Out of 112 students, 66 studied in the library, 54 studied in the student union and 23 studied in both places. How many students did NOT study in either the library or student union?







I'm taking 23 out of the equation because they studied in both places.

66-23 = 43
54-23 = 31

43+31 = 74

112-74 = 38 students did not study in the library or student union.
 
gardenia said:
Am I solving this problem correctly?

A survey was taken to determine where students study. Out of 112 students, 66 studied in the library, 54 studied in the student union and 23 studied in both places. How many students did NOT study in either the library or student union?


I'm taking 23 out of the equation because they studied in both places.

66-23 = 43
54-23 = 31

43+31 = 74

112-74 = 38 students did not study in the library or student union.
Click to expand...

Not quite:

Number students that studied either at the library OR at the union = 66 + 54 - 23 = 97

Number students that studied neither at the library NOR at the union = 112 - 97 = 15
 
gardenia said:
Am I solving this problem correctly?

A survey was taken to determine where students study. Out of 112 students, 66 studied in the library, 54 studied in the student union and 23 studied in both places. How many students did NOT study in either the library or student union?

I'm taking 23 out of the equation because they studied in both places.

66-23 = 43
54-23 = 31

43+31 = 74

112-74 = 38 students did not study in the library or student union.
Click to expand...
You should take the 23 out once, not twice. If you add together the library and the union, you will have counted the overlap twice - so you have to subtract it once:

library or union or both = 66 + 54 - 23 = 97

"neither" = 112 - 97 = 15
 
Or: students who studied ONLY in the library: 43. Students who studied ONLY in the student union: 31. Students who studied in BOTH: 23. Students who studied in the library or student union or both:43+ 31+ 23= 97.

Students who studied in neither: 112- 97= 15.
 
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