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Total Membership

```
Date: 08/20/99 at 20:51:06
From: Geryca Foy
Subject: What is the correct answer?

At a country club 35 people play golf, 28 swim, and 24 play tennis. Of
these people, 6 play golf and tennis only, 9 play golf and swim only,
and 7 play tennis and swim only. 8 people do all three activities. How
many members are there altogether?

My teacher did the problem and the answer she gave us was 29, using a
diagram. I don't understand how there can be fewer members in the
country club than there are people playing golf.
```

```
Date: 08/20/99 at 22:36:08
From: Doctor Peterson
Subject: Re: What is the correct answer?

Hi, Geryca.

You probably copied the answer incorrectly. It should be 49, which
makes more sense. Here's the diagram:

...........  ***********
golf   ....         **....         ****   swim
..           **      ..           **
.            *    9     .            *
.    (12)    *            .     (4)    *
.            * -----------.            *
.          --*-           .---         *
.        --  *     8      .   --       *
.      -     *          .      -     *
..   -   6   **      ..   7    -  **
...-         **....         *-**
-...........  *********** -
-                         -
-          (3)          -
--                   --
----           ----
-----------

tennis

The numbers in parentheses were filled in last, by subtracting the
given numbers from the total for each activity. Then I just added the
numbers up.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Discrete Mathematics
High School Sets

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