jmc

To make this easier, you can scale all the student numbers down by a factor of 6: 5 students averaged a $72\%$, and 1 student got a $78\%$. Then, instead of adding that up, you note, since 5 students averaged a 72, and only 1 student got a 78, the class average should be 5 times closer to 72 than 78. And since $78-72=6$, we perfectly get $\boxed{73\%}$ as the class average, since $73-72=1$, and $78-73=5$.