A friend has a \( 84 \% \) average before the final exam for a course. That score includes everything but the final, which counts for \( 15 \% \) 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? Give answers accurate to at least one decimal place.

To determine your friend's course grade based on their pre-final average and final exam score, we'll break down the calculations step by step. ### 1. **Best Possible Course Grade** The overall course grade is a combination of the pre-final average and the final exam score. Here's how it's calculated: - **Pre-Final Average Contribution:** 84% of the course grade contributes **85%** (since the final is 15%). - **Final Exam Contribution:** The final exam counts for **15%** of the course grade. **Calculation:** \[ \text{Overall Grade} = (84 \times 0.85) + (100 \times 0.15) = 71.4 + 15 = 86.4\% \] **Best Possible Course Grade:** **86.4%** ### 2. **Minimum Final Exam Score for a 75% Course Grade** To achieve a **75%** overall course grade, we need to find the minimum score required on the final exam. **Setting Up the Equation:** \[ 75 = (84 \times 0.85) + (X \times 0.15) \] \[ 75 = 71.4 + 0.15X \] \[ 75 - 71.4 = 0.15X \] \[ 3.6 = 0.15X \] \[ X = \frac{3.6}{0.15} = 24 \] **Minimum Final Exam Score Needed:** **24.0%** --- **Summary:** - **Best Possible Course Grade:** 86.4 % - **Minimum Final Exam Score for a 75 % Course Grade:** 24.0 %