Question

A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 30% of the course grade.

A : What is the best course grade your friend can earn?

B: What is the minimum score would your friend would need on the final to earn a 75% for the course?

Give answers accurate to at least one decimal place.

Answer 1

The best course grade the student can achieve is 88.1% if they score 100% on the final. To earn a 75% in the course, the student needs a minimum of 56.3% on the final exam.

Step-by-step explanation:

Calculating the Best Possible Course Grade and Minimum Required Final Exam Score

To determine the best course grade your friend can earn, we need to calculate the maximum score on the final exam and how it would impact the overall course grade. Assuming your friend scores a perfect 100% on the final, which accounts for 30% of the overall course grade:

Overall grade = current average × (1 - weight of final exam) + score on final × weight of final exam

Overall grade = 83% × (1 - 0.30) + 100% × 0.30

Overall grade = 83% × 0.70 + 100% × 0.30

Overall grade = 58.1% + 30%

Overall grade = 88.1%

The best course grade your friend can earn is 88.1%.

To find the minimum score needed on the final to earn a 75% for the course, we can use the same formula but solve for the final exam score:

75% = 83% × 0.70 + final exam score × 0.30

75% - 58.1% = final exam score × 0.30

16.9% = final exam score × 0.30

final exam score = 16.9% / 0.30

final exam score = 56.3%

Your friend needs a minimum of 56.3% on the final exam to earn a 75% overall course grade.

Answer 2

• 88.1%
• 56.3%

Step-by-step explanation:

If f represents the score on the final exam, the final grade (g) is ...

g = 83%×0.70 + f×0.30

g = 58.1% + 0.30f

A. If f is 100%, then the resulting final grade is

g = 58.1% + 0.30×100% = 88.1%

__

B. To earn 75%, the grade on the final would need to be ...

75% = 58.1% + 0.30f

16.9% = 0.30f

16.9%/0.30 = f ≈ 56.3%