# Interesting question

• Sep 5th 2013, 11:51 PM
saunak
Interesting question
Suppose 150 people joined 3 different communities in Google+. The communities are for 1. Mathematics, 2. Hot Peppers and 3. Cooking

Here is what is known:

1. 90 joined Mathematics community
2. 50 joined Hot Peppers community
3. 70 joined Cooking community
4. 15 joined Mathematics and Cooking both
5. 12 joined Hot Peppers and Cooking
6. 10 joined all three communities.

The question is how many joined Mathematics and Hot Peppers (both my favorite) communities.

• Sep 6th 2013, 03:53 PM
Soroban
Re: Interesting question
Hello, saunak!

Quote:

Suppose 150 people joined 3 different communities in Google+.
The communities are: Mathematics, Hot Peppers and Cooking.

Here is what is known:

1. 90 joined Mathematics community
2. 50 joined Hot Peppers community
3. 70 joined Cooking community
4. 15 joined both Mathematics and Cooking
5. 12 joined both Hot Peppers and Cooking
6. 10 joined all three communities.

How many joined Mathematics and Hot Peppers only?

Let $x$ = number in Math and Peppers only.
Fill in the Venn diagram.

It should look like this . . .

Code:

```              o o o          o o o           o          o  o          o         o    Math      o    Peppers    o       o              o o              o                         x       o    75-x      o  o    38-x      o       o              o o o              o       o          o  o  o  o          o                 o      10      o       o      o      o o      o      o         o        5    o    2        o           o  o      o  o      o  o               o o o          o o o               o                  o                         53               o                o                 o    Cooking    o                   o          o                       o o o```
The total of the numbers is 150.

$(75-x) + x + (38-x) + 5 + 10 + 2 + 53 \:=\:150$

. . . . . . $-x + 183 \:=\:150$

Therefore: . $x \:=\:33$