AMC 10 2021-fall-a Problem 10

A school has $100$ students and $5$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50, 20, 20, 5,$ and $5$. Let $t$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let $s$ be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is $t-s$? $\textbf{(A)}\ {-}18.5 \textbf{(B)}\ {-}13.5 \textbf{(C)}\ 0 \textbf{(D)}\ 13.5 \textbf{(E)}\ 18.5$