https://file.aiquickdraw.com/mathbot/file/1729819651372c2eg4uzi.jpg

Let's break down and solve the problem from your screenshot.

### Problem 1: Best course grade your friend can earn

- **Given**:
  - Current average: 83%
  - The final exam counts for 25% of the course grade.
  
The course grade \( G \) is calculated as a weighted average:

\[
G = (0.75 \times 83) + (0.25 \times \text{Final Exam Score})
\]

The highest possible final exam score is 100%, so we substitute that into the formula:

\[
G = (0.75 \times 83) + (0.25 \times 100)
\]

\[
G = 62.25 + 25 = 87.25
\]

So, the best course grade your friend can earn is **87.3%** (rounded to one decimal place).

### Problem 2: Minimum score on the final to earn a 75% overall

We need to determine the minimum final exam score needed to achieve a 75% course grade. Set \( G = 75 \) in the same formula:

\[
75 = (0.75 \times 83) + (0.25 \times \text{Final Exam Score})
\]

Simplify:

\[
75 = 62.25 + 0.25 \times \text{Final Exam Score}
\]

Subtract 62.25 from both sides:

\[
12.75 = 0.25 \times \text{Final Exam Score}
\]

Solve for the Final Exam Score:

\[
\text{Final Exam Score} = \frac{12.75}{0.25} = 51
\]

So, your friend needs a minimum score of **51%** on the final to earn a 75% overall grade.

---

Would you like more details or have any questions? 

Here are 5 related questions to expand on this:
1. What if the final exam accounted for 40% of the grade instead of 25%?
2. How would the result change if the current average was 90%?
3. What is the final score needed to achieve an overall grade of 85%?
4. How would missing the final exam entirely affect the final grade?
5. Can your friend achieve a 90% overall grade, and what score would be needed?

**Tip:** Always double-check that you're using the correct percentage weighting for different grade components when calculating final grades!

A friend has an 83% average before the final exam for a course. That score includes everything but the final, which counts for 25% of the course grade. What is the best course grade your friend can earn? What is the minimum score your friend would need on the final to earn a 75% for the course?

Learn how to calculate the best and minimum final exam scores required to reach a target course grade. This problem involves weighted averages, algebra, and percentage calculations, suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation