A class of 40 students averaged 90% on a test. Another class of 20 students averaged 96% on the same test. What is the combined average for both classes?

Question

A class of 40 students averaged 90% on a test. Another class of 20 students averaged 96% on the same test. What is the combined average for both classes?

 

PLEASE HELP

Answer 1

I would think of this as 40 students each scoring a 90 and 20 students scoring a 96 on the test.  

 

You have a total of 60 students.

 

(40 * 90 + 20 * 96) / 60 = the combined average.

 

(3600 + 1920) / 60 = 5520 / 60 = 92% for the combined average.

 

Let me know if this doesn't make sense.

Answer 2

Average = (total of scores) / (number of students)

 

Number the scores s1 to s60.

 

For the class of 40:

    90 = (s1+s2+s3+...+s40)/40      [eq1]

For the class of 20:

    96 = (s41+s42+s43+...+s60)/20      [eq2]

For the combined classes:

    x = (s1+s2+s3+...s40+s41+s42+s43+...+s60)/60   [eq3]

 

The math:

    60x = (s1+s2+s3+...s40+s41+s42+s43+...+s60)   [from eq3]

    60x = (s1+s2+s3+...s40) + (s41+s42+s43+...+s60)

    60x = 40*90                      + 20*96           [use eq1 and eq2]

    60x = 5520

      x  = 92

  The average of all 60 students is 92%.