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
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-> 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
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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?
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
