Venn Diagram: survey of college students and study areas

[patti72458]

Need help with a venn diagram

At a local college a survey was taken determine where students studied on campus. Of 160 students surveyed it was determined that 79 studied in the library, 65 studied in the student lounge and 43 studied in both the library and student lounge.
of those interviewed
a) how many studied in only the library?
b) how many studied in only the student lounge?
c) how many did not study in either location?

please help with a venn diagram

 

[tkhunny]

Draw two overlapping circles and enclose them in a box.

The box represents the 160 students.

Lable one of the circles "Library". Lable the other "Lounge".

You should see that each of these is divided into to pieces, one of which they share. The shared piece represents the 43 that study in BOTH. Can you assign the other two numbers to available spaces?

 

[soroban]

Re: Venn Diagram

Hello, patti!

If you need help with this one (the simplest Venn diagram problem),
. . I assume you're just starting the topic.
I'll walk through it for you . . . with baby-steps.

At a local college, a survey was taken to determine where students studied on campus.
Of 160 students surveyed it was determined that:
79 studied in the library, 65 studied in the student lounge
and 43 studied in both the library and student lounge.

Of those interviewed:
a) how many studied in only the library?
b) how many studied in only the student lounge?
c) how many did not study in either location?

Draw two overlapping circles. .Label one "Library", the other "Lounge".
Draw a rectangle around them. .This represents the entire 160 students.
There are four numbered regions in the Venn diagram.

      *-----------------------------------------------*
      |                                               |
      |           *-------*       *-------*           |
      |         /  Library  \   /  Lounge   \         |
      |       /               ×               \       |
      |     /               /   \               \     |
      |   *               *       *               *   |
      |   |               |       |               |   |
      |   |       [1]     |  [2]  |     [3]       |   |
      |   |               |       |               |   |
      |   *               *       *               *   |
      |     \               \   /               /     |
      |       \               ×               /       |
      |         \           /   \           /         |
      |           *-------*       *-------*     [4]   |
      |                                               |
      *-----------------------------------------------*

43 students studied in both the Library and the Lounge.
. . Write "43" in regrion [2].

      *-----------------------------------------------*
      |                                               |
      |           *-------*       *-------*           |
      |         /  Library  \   /  Lounge   \         |
      |       /               ×               \       |
      |     /               /   \               \     |
      |   *               *       *               *   |
      |   |               |       |               |   |
      |   |       [1]     |  43   |     [3]       |   |
      |   |               |       |               |   |
      |   *               *       *               *   |
      |     \               \   /               /     |
      |       \               ×               /       |
      |         \           /   \           /         |
      |           *-------*       *-------*     [4]   |
      |                                               |
      *-----------------------------------------------*

79 students studied in the Library.
. . We have accounted for 43 of them.
Hence, there are: .\(\displaystyle 79\,-\,43\:=\:36\) in region [1].
. . (a) Therefore, 36 students studied in the Library only.

      *-----------------------------------------------*
      |                                               |
      |           *-------*       *-------*           |
      |         /  Library  \   /  Lounge   \         |
      |       /               ×               \       |
      |     /               /   \               \     |
      |   *               *       *               *   |
      |   |               |       |               |   |
      |   |       36      |  43   |     [3]       |   |
      |   |               |       |               |   |
      |   *               *       *               *   |
      |     \               \   /               /     |
      |       \               ×               /       |
      |         \           /   \           /         |
      |           *-------*       *-------*     [4]   |
      |                                               |
      *-----------------------------------------------*

65 students studied in the Lounge.
. . We have accounted for 43 of them.
Hence, there are 22 students in region [3].
. . (b) Therefore, 22 students studied in the Lounge only.

      *-----------------------------------------------*
      |                                               |
      |           *-------*       *-------*           |
      |         /  Library  \   /  Lounge   \         |
      |       /               ×               \       |
      |     /               /   \               \     |
      |   *               *       *               *   |
      |   |               |       |               |   |
      |   |       36      |  43   |     22        |   |
      |   |               |       |               |   |
      |   *               *       *               *   |
      |     \               \   /               /     |
      |       \               ×               /       |
      |         \           /   \           /         |
      |           *-------*       *-------*     [4]   |
      |                                               |
      *-----------------------------------------------*

We have accounted for: \(\displaystyle \:36\,+\,43\,+\,22\:=\:101\) students.

This leave: \(\displaystyle \:160\,-\,101\:=\:59\) students for region [4].
. . (c) Therefore, 59 students studied in neither location.

      *-----------------------------------------------*
      |                                               |
      |           *-------*       *-------*           |
      |         /  Library  \   /  Lounge   \         |
      |       /               ×               \       |
      |     /               /   \               \     |
      |   *               *       *               *   |
      |   |               |       |               |   |
      |   |       36      |  43   |     22        |   |
      |   |               |       |               |   |
      |   *               *       *               *   |
      |     \               \   /               /     |
      |       \               ×               /       |
      |         \           /   \           /         |
      |           *-------*       *-------*     59    |
      |                                               |
      *-----------------------------------------------*

 

[tkhunny]

Patti, if you get an answer that looks like this:

library = 23 loungs = 34 (I just made up the numbers)

Then you don't yet get it. That is just the sort of information you were given. You must differentiate between "lounge" in general and "lounge only".