A​ student's course grade is based on one midterm that counts as 10​% of his final​ grade, one class project that counts as 25​% of his final​ grade, a set of homework assignments that counts as 40​% of his final​ grade, and a final exam that counts as 25% of his final grade. His midterm score is 67​, his project score is 96​, his homework score is 78​, and his final exam score is 62. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.

To calculate the student's overall final score, we will use the weighted average formula based on the different components of the final grade.

Given:

- **Midterm** = 67 (10% of the final grade)
- **Project** = 96 (25% of the final grade)
- **Homework** = 78 (40% of the final grade)
- **Final Exam** = 62 (25% of the final grade)

The formula for the final score is:

\[
\text{Final Score} = (\text{Midterm} \times 0.10) + (\text{Project} \times 0.25) + (\text{Homework} \times 0.40) + (\text{Final Exam} \times 0.25)
\]

Substituting the given values:

\[
\text{Final Score} = (67 \times 0.10) + (96 \times 0.25) + (78 \times 0.40) + (62 \times 0.25)
\]

Now calculating each term:

\[
67 \times 0.10 = 6.7
\]
\[
96 \times 0.25 = 24
\]
\[
78 \times 0.40 = 31.2
\]
\[
62 \times 0.25 = 15.5
\]

Summing these values:

\[
6.7 + 24 + 31.2 + 15.5 = 77.4
\]

So, the student's **overall final score** is **77.4**.

Now, to determine the letter grade:

- **A**: 90 or above
- **B**: 80 to less than 90
- **C**: 70 to less than 80
- **D**: 60 to less than 70
- **F**: Less than 60

Since the student's final score is **77.4**, this falls into the **C** range.

Thus, the student earns a **C**.

---

Would you like more details or have any questions?

Here are 5 related questions you might consider:

1. How can we calculate a weighted average for a different grading system?
2. How would the grade change if the student improved their final exam score?
3. What if each component of the grade had different weightings?
4. How do you handle grades if they are curved?
5. How would dropping the lowest homework score impact the final grade?

**Tip**: Always verify the weightings add up to 100% when calculating weighted averages.

A student's course grade is based on one midterm that counts as 10% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 40% of his final grade, and a final exam that counts as 25% of his final grade. His midterm score is 67, his project score is 96, his homework score is 78, and his final exam score is 62. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.

Learn how to calculate a final grade using weighted averages. This problem involves midterm, project, homework, and final exam scores, applying percentages to determine the overall final score. The solution includes how to assign a letter grade based on the final score. Suitable for Grades 8-10 students.

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