A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 30% of the course grade.
If your friend scores 100% on the final exam, their overall course grade would be:
0.81(70%) + 0.30(100%) = 56.7% + 30% = 86.7%
Therefore, if your friend scores perfectly on the final exam, their overall course grade would be 86.7%.
To calculate your friend's final grade, you need to consider two components: their average before the final exam and the weight of the final exam in determining the course grade.
Step 1: Calculate the weight of the average before the final exam
Since the average before the final exam counts for 70% of the course grade (100% - 30%), you multiply the average by 0.70 to determine its weight.
Weight of the average = 81% × 0.70 = 56.7%
Step 2: Calculate the weight of the final exam
As mentioned, the final exam counts for 30% of the course grade.
Weight of the final exam = 30%
Step 3: Calculate the final grade
To determine the final grade, you need to combine the weighted average before the final exam and the weighted final exam grade.
Final grade = Weight of the average + Weight of the final exam
Final grade = 56.7% + 30% = 86.7%
Therefore, your friend's final grade for the course would be 86.7%.