Can You Crack This Challenging Math Puzzle?

[adventuretime]

Homework Statement

[PLAIN]http://img408.imageshack.us/img408/5284/scan0003xp.jpg

Homework Equations

There are none?

The Attempt at a Solution

I have tried to solve this problem via making a graph, trying to outright solve the problem, i have also tried to assign variables, and logically think the problem through.

 

[ebits21]

Edit:

I just noticed this is a take home exam, so I'm only going to give you a vague hint.

You know you have three categories, and you know that those categories overlap. Is there anything you learned in class that could visually show 3 overlapping categories?

 

[adventuretime]

Thank you very much, I was able to solve this particular problem with your hint :)