Finding average arithmetic mean

Question

On the midterm exam, the average grade of a class was 86. If 20% of the class averaged 95, and 30% of class averaged 90, what was the average grade of the rest?

Answer 1

This is an application of the weighted arithmetic mean.  The score of 95% gets a 20% weight (0.20), the score of 90% gets a 30% (0.30) weight, and the "rest of the class" gets the remaining 50% (0.50) weight.  Let x = the average grade of the rest of the class:

 

(0.2)(95%) + (0.3)(90%) + (0.5)(x%) = 86%

 

19% + 27% + 0.5x = 86%

 

0.5x = 40%

 

Solve for x.

 

 

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