A college physics class has n registered students-all of whom are either freshmen or sophomores. On the first midterm, the average score of the 60 freshmen was 72, and the average score of the sophomores was 80. What is the value of n if the overall average score was 75?

n is 96

Step-by-step explanation:

Firstly, we know that the total number of registered students is n. Since there are 60 freshmen, the number of sophomores would be (n - 60).

The total score of the freshmen is 60 * 72 = 4,320

The total score of the sophomores is 80 (n - 60)

The total score of all the registered students is 75 * n = 75n

We know that if we add the score of the freshmen to the score of the sophomores, we will get the total score of 75n

Mathematically, this means:

4,320 + 80 (n - 60) = 75n

4,320 + 80n - 4800 = 75n

4800 - 4320 = 80n - 75n

5n = 480

n = 480/5 = 96

The total number of registered students is 96