SOLUTION: Three math classes: A,B,C Taken a test. The avg score of A is=83. The avg score of B is=76. The avg score of C is=75. The avg score of all students in classes A & B together is

Question 980736: Three math classes: A,B,C Taken a test.
The avg score of A is=83.
The avg score of B is=76.
The avg score of C is=75.
The avg score of all students in classes A & B together is 67
The avg score of all students in classes B & C together is 81.
I) What is the avg of all 3 classes?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have an error in the way you have written this question. In order for the numbers you have presented to be true, one of the classes would necessarily have a negative number of students.

Let

be the number of students in Class A. Then the total of all scores in Class A must be

since the total of all scores in Class A divided by the number of students in Class A is 83 by definition of "average".

Likewise, if

is the number of students in Class B, the total of all scores in Class B must be

.

And furthermore, since

is the number of students in Class A and Class B and the average of these two classes is 67, the total score of both classes must be

.

And finally, the total scores of Class A plus the total scores of Class B must equal the total scores of both classes, that is:

A little algebra:

and the only way for this statement to be true is if one of

and

is negative. Division by zero precludes zero students in any of the classes.

A similar result is obtained when Class B and Class C are compared.

In order for this problem to work out is if the combined A and B average is a number between 83 and 76 and the combined B and C average is a number between 76 and 75.

John

My calculator said it, I believe it, that settles it

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