A class of 30 students took a science test. 10 students had an average (arithmetic mean) score of 85. The other students had an average score of 70. What is the average score of the whole class?

So you need to calculate a weighted average, where the average of 70 has twice the weight of the average of 85 (20 students vs 10). The easiest way to think about it is to split the 20 into two groups of 10 so that you have three groups of 10 students, that way you can just average the scores as normal.

So, you have three averages of 85, 75 and 75.

Total average = (85+75+75) / 3 = 78.33 ...