manik11 wrote:The final exam of a particular class makes up 40% of the final grade, and Moe is failing the class with an average (arithmetic mean) of 45% just before taking the final exam. What grade does Moe need on his final exam in order to receive the passing grade average of 60% for the class?
A) 75%
B) 82.5%
C) 85%
D) 90%
E) 92.5%
sum = (weight)(average).
Let the total weight of the course = 100.
Since the final constitutes 40% of the course, the weight of the final = 40.
Thus, the pre-final weight = 100-40 = 60.
To yield a course average of 60, the sum for the course = (course weight)(course average) = (100)(60) = 6000.
Since the pre-final average = 45, the pre-final sum = (pre-final weight)(pre-final average) = (60)(45) = 2700.
Thus:
Sum for the final = (course sum) - (pre-final sum) = 6000-2700 = 3300.
Average for the final = (sum for the final)/(weight of the final) = 3300/40 = 82.5.
The correct answer is
B.
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