In a class of $30$ students, exactly $7$ have been to Mexico and exactly $11$ have been to England. Of these $30$ students, $4$ have been to both Mexico and England. How many students in this class have not been to Mexico or England?
I could start by drawing a Venn diagram to represent the situation, with two overlapping circles for Mexico and England and a rectangle for the class. The region where the circles overlap represents the students who have been to both countries, so I can label that with $4$. The region where only the Mexico circle is shaded represents the students who have been to Mexico but not England, so I can label that with $7 - 4 = 3$. Similarly, the region where only the England circle is shaded represents the students who have been to England but not Mexico, so I can label that with $11 - 4 = 7$. So I can write an equation: $4 + 3 + 7 + x = 30$, where $x$ is the number I want to find. Solving for $x$, I get $x = 30 - 4 - 3 - 7 = 16$. Therefore, the answer is that $16$ students in this class have not been to Mexico or England. 