2021 AMC 10B 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 \qquad\textbf{(B)} ~75 \qquad\textbf{(C)} ~76 \qquad\textbf{(D)} ~77 \qquad\textbf{(E)} ~78

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.