Let's say there are 5 students with a score of 750 and 8 students with a score of 780. And if their combined average score for the class of 13 students is m, then the relationship between the quantities is as follows:
(780-m)/(m-750) = 5/8
Note 780 -m is the distance of the combined average from one end and m-750 is the distance from the other end. These quantities are in the same ratio as the weights on the opposite ends(here the number of students).
And the above equation is merely a rearrangement of the basic definition of the weighted average, which in this case would give us the average explicitly:
m = [8(780) + 5(750)]/[8+5]
Try rewriting this above equation in to the form of the first equation.
Cheers,
Dabral