Question

Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean) score for the two classes combined was 84. Which class had more students?(1) The average score for the students in the morning class was 80
(2) the average score for the students in the afternoon class was 86

Answer 1

Answer:

Afternoon class has more students.

Step-by-step explanation:

Let m be the number of students in the morning class and n be the number of students in the afternoon class.

The average score for the students in the morning class was 80, then the sum of their scores is $80m.$

The average score for the students in the afternoon class was 86, then the sum of their scores is $86n.$

The sum of the scores of both classes is

$80m+86n$

and the average score is

$\dfrac{80m+86n}{m+n}$

The average (arithmetic mean) score for the two classes combined was 84, then

$\dfrac{80m+86n}{m+n}=84\\ \\ 80m+86n=84m+84n\\ \\86n-84n=84m-80m\\ \\2n=4m\\ \\n=2m$

This means n is greater, so afternoon class has more students.