A survey was made of 200 students to study their use of the public library system. The findings were as follows:

60 used the Reader’s Guide.
28 used both the card catalog and the information booth.
68 used the information booth.
83 did not use the library.
43 used only the card catalog

Explain how the above information can be used to conclude that some students must use both the information booth and the Reader’s Guide.

200 - 83 = 117 use the library

60 + 28 + 68 = ?

156

To determine if some students must use both the information booth and the Reader's Guide, we need to analyze the given information.

Let's break down the given information one by one:

- 60 students used the Reader’s Guide.
- 28 students used both the card catalog and the information booth.
- 68 students used the information booth.
- 83 students did not use the library.
- 43 students used only the card catalog.

To find the number of students who have used the information booth only, we subtract the number of students who used both the card catalog and information booth (28) from the total number of students who used the information booth (68).
So, the number of students who used the information booth only is 68 - 28 = 40.

Next, we can find the number of students who used both the Reader's Guide and the information booth by subtracting the number of students who used the card catalog only (43) from the total number of students who used the information booth (68).
So, the number of students who used both the Reader's Guide and the information booth is 68 - 43 = 25.

Now, to determine if some students must use both the information booth and the Reader's Guide, we need to see if the number of students who used both (25) is greater than zero. Since 25 is indeed greater than zero, we can conclude that some students must use both the information booth and the Reader's Guide.

Therefore, based on the given information, we can conclude that there are students who utilize both the information booth and the Reader's Guide.