The average age of $33$ fifth-graders is $11$. The average age of $55$ of their parents is $33$. What is the average age of all of these parents and fifth-graders?

$\textbf{(A) }22\qquad\textbf{(B) }23.25\qquad\textbf{(C) }24.75\qquad\textbf{(D) }26.25\qquad\textbf{(E) }28$
1. First, we need to find the total age of the fifth-graders. Given that the average age of 33 fifth-graders is 11, we can calculate the total age as follows:
   \[
   \text{Total age of fifth-graders} = 33 \times 11 = 363
   \]

2. Next, we need to find the total age of the parents. Given that the average age of 55 parents is 33, we can calculate the total age as follows:
   \[
   \text{Total age of parents} = 55 \times 33 = 1815
   \]

3. Now, we need to find the combined total age of all the fifth-graders and their parents:
   \[
   \text{Combined total age} = 363 + 1815 = 2178
   \]

4. We also need to find the combined total number of individuals (fifth-graders and parents):
   \[
   \text{Total number of individuals} = 33 + 55 = 88
   \]

5. Finally, we can find the average age of all these individuals by dividing the combined total age by the total number of individuals:
   \[
   \text{Average age} = \frac{2178}{88} = 24.75
   \]

Conclusion:
\[
\boxed{24.75}
\]