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.

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UpStudy AI · Accepted Answer

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 %
- **Best Possible Course Grade:** 86.4% - **Minimum Final Exam Score Needed for a 75% Course Grade:** 24.0%

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