To determine the scores Trent can earn on the final exam to pass the course with a "C" or better, we can break down the problem step by step. We know that Trent needs an overall course score of at least 70, and we need to compute the contributions of each component of the course grade.

1. Breakdown of the formula for the overall course score:

The overall course score is calculated as follows:

• Average of the three chapter tests: 40% of the total grade.
• Homework score: 20% of the total grade.
• Project score: 20% of the total grade.
• Final exam score: 20% of the total grade.

So, the total grade $G$ is given by: $G = 0.40 \times \text{(Average of the chapter tests)} + 0.20 \times \text{Homework} + 0.20 \times \text{Project} + 0.20 \times \text{Final Exam}$

2. Compute Trent's current contributions (without the final exam):

Chapter Tests:

Trent's scores on the three chapter tests are 69, 80, and 72. The average of these scores is: $\text{Average of chapter tests} = \frac{69 + 80 + 72}{3} = \frac{221}{3} \approx 73.67$

The contribution of the chapter tests to the overall grade is: $\text{Chapter test contribution} = 0.40 \times 73.67 = 29.47$

Homework:

Trent's homework grade is 64, and its contribution is: $\text{Homework contribution} = 0.20 \times 64 = 12.8$

Project:

Trent's project grade is 63, and its contribution is: $\text{Project contribution} = 0.20 \times 63 = 12.6$

3. Set up the inequality to solve for the final exam score:

Let $x$ be the score Trent earns on the final exam. The contribution of the final exam is: $\text{Final exam contribution} = 0.20 \times x$

To pass the course with a "C" or better, Trent needs an overall score of at least 70. Therefore, we set up the following inequality: $29.47 + 12.8 + 12.6 + 0.20x \geq 70$

4. Solve for $x$:

Simplify the inequality: $54.87 + 0.20x \geq 70$

Subtract 54.87 from both sides: $0.20x \geq 70 - 54.87$ $0.20x \geq 15.13$

Now, divide both sides by 0.20: $x \geq \frac{15.13}{0.20} = 75.65$

Since only whole-number scores are allowed, Trent must score at least 76 on the final exam to achieve an overall course grade of 70 or better.

Conclusion:

To pass the course with a "C" or better, Trent needs to score at least 76 on the final exam. The highest score he can earn is 100.

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Would you like more details, or do you have any other questions?

5 Related Questions:

1. How would the required final exam score change if Trent had different chapter test scores?
2. What would happen if Trent could retake the homework assignment and improve his score?
3. How is the impact of each course component calculated, and why does the final exam have a significant influence on the overall grade?
4. What if the grading weights were adjusted? How would that affect Trent's final score?
5. If Trent scored exactly 76, what would his overall course grade be?

Tip:

Always check the weight of each component in a weighted average calculation to see how much influence each score has on the overall grade.