A school is arranging chairs in rows for an assembly. $11$ chairs make a complete row, and right now there are $110$ chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If $70$ students will attend the assembly, how many chairs should be removed?
I want to find the number of chairs that should be removed, so I need to compare the current number of chairs to the ideal number of chairs. The ideal number of chairs is the smallest multiple of $11$ that is greater than or equal to $70$, since that would make all rows complete and have as few empty seats as possible. To find the smallest multiple of $11$ that is greater than or equal to $70$, I can divide $70$ by $11$ and round up to the next integer. That is, $\frac{70}{11} \approx 6.36$, so the smallest multiple of $11$ that is greater than or equal to $70$ is $7 \times 11 = 77$. Therefore, the ideal number of chairs is $77$, and the number of chairs that should be removed is the difference between the current number of chairs and the ideal number of chairs. That is, $110 - 77 = 33$. 