A class of 40 students took a math test 18 of the students had a weighted average of 80. The other students had a weighted average of 70. What is the average score of the whole class? A) 74 B) 74.5 C) 76 D) 76.5​

Explanation:

Average = (sum of scores)/(number of scores)

We can turn that equation into symbolic form to say

A = S/n

We're told that "18 students had an average of 80" (paraphrased) which means,

A = S/n

80 = S/18

80*18 = S

S = 1440

Those 18 students' scores add up to 1440.

For the other group of 40-18 = 22 students, their scores add to

S = A*n

S = 70*22

S = 1540

Overall, everyone's scores add up to 1440+1540 = 2980

Divide this over the number of people in class (40) to get the final answer

2980/40 = 74.5

Here's an alternative way to compute the answer

(18/40)*80 + (22/40)*70 = 74.5

This works because 18/40 of the class got an average of 80 while the remaining 22/40 of the class got an average of 70.