Question 104878: 60% of a student's final grade is equal to a 2.75 (averaged from four quizzes). The remaining 40% of the final grade is to be taken from the score received on a final exam. What score does the student need to get on the final exam in order to achieve an overall grade of 2.0 or better?
I couldn't figure this one out due to the weighted averages....
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! The total of the weights must be 1.00.
We are gold that .6 of the final grade is based on 4 quizzes, and that the average is 2.75. That means that the total of the 4 quizzes, divided by 4 and then multiplied by .6 = 2.75. So .6x = 2.75. Multiplying by 100 to remove the decimals, we have 60x = 275. Dividing by 60, we suddenly see that x > 4.0, which is not likely the case.
Therefore, I will assume the average of the 4 quizzes is 2.75. This value will be weighted at 60% of the final grade.
We also are told that the desired final average must be at least 2.0.
Creating an equation of what we know:
.6(2.75)+.4(x)=2.0.
Again, the decimals can be removed by mulplying by 100. If you are using a calculator, you may not need to do this.
60(2.75)+40x=200
165+40x=200
Subtracting 165 from both sides:
40x = 35
Dividing by 40:
x = 35/40 = 7/8 = .875
That means the student can crater the final exam, getting a 0.875 out of 4.00 is perhaps an D-, and still have a C average (2.0) for the course.
Logic tells us that makes sense. The student has nearly a B- average (2.75) for 60% of the grade. So to pull the final grade down to a C, the 20% final exam must be pretty bad.
ALWAYS check your solutions!
.6(2.75)+.4(.875) = ?
1.65 + .35 = 2.00.
Check!
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