Question

at a community college a survey was taken to determine where students study on campus. Of the 270 students surveyed, it was determined that 177 studied in the library , 142 studied in the cafeteria, 82 studied in both the library and the cafeteria. Of those students surveyed, how many studied only in the library?

Answer 1

95

Explanation:

Use a Venn diagram;

2 places are identified where students may study, the library and the cafeteria so there are 2 circles;

One represents library (L) and the other is cafeteria (C);

82 goes in the overlap since 82 study in both places;

177 study in the library, but this includes the 82 that also study in the cafeteria, so 177 - 82 will give us the number who study only in the library, i.e. 95;

If we wanted to find the number who study only in the cafeteria, it would be similar;

142 study in cafeteria, including the 82 who also study in the library, therefore 142 - 82 will give the number who only study in the cafeteria, i.e. 60;

The number who study in neither the library nor the cafeteria would be the total number of students surveyed (270) take the 82 who study in both places and take the 95 who study only in the library and take the 60 who study only in the cafeteria, which gives 33 (i.e. 270 - 82 - 95 - 60)

Answer 2

177

Explanation:

Although it says that 82 studied in both, the question is aksing for ONLY at the library. It says that of the 270 surveyed, 177 study at the library.

This means that 65.56% of the students studied at the library primarely.