How to Deal with Venn Diagrams
This blog post is primarily for my niece Katya, who was asked this nice problem in her homework:
In a camp, there are 79 kids; 27 of them are younger than twelve, 33 are girls, and 30 are boys that are twelve or older. Fill in this chart:
Girls | Boys | All | |
Younger than twelve | |||
Twelve or older | |||
All |
The real question was to demonstrate that this chart can only be filled in only one possible way. So great, let's first enter in what we know:
Girls | Boys | All | |
Younger than twelve | 27 | ||
Twelve or older | 30 | ||
All | 33 | 79 |
Now, since the "All" must be equal to the sum of the parts, you have enough information to find out two of the cells, namely
Girls | Boys | All | |
Younger than twelve | 27 | ||
Twelve or older | 30 | I must be 79-27=52 | |
All | 33 | I must be 79-33=46 | 79 |
Now we're here:
Girls | Boys | All | |
Younger than twelve | 27 | ||
Twelve or older | 30 | 52 | |
All | 33 | 46 | 79 |
Then there are two more cells we know:
Girls | Boys | All | |
Younger than twelve | I must be 46-30=16 | 27 | |
Twelve or older | I must be 52-30=22 | 30 | 52 |
All | 33 | 46 |