AMC 10 2021b Problem 6

Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is $84$, and the afternoon class's mean score is $70$. The ratio of the number of students in the morning class to the number of students in the afternoon class is $\frac{3}{4}$. What is the mean of the scores of all the students? $\textbf{(A)} ~74 \textbf{(B)} ~75 \textbf{(C)} ~76 \textbf{(D)} ~77 \textbf{(E)} ~78$