To calculate Mariah's overall grade in her algebra course, we will use a weighted average based on the percentage breakdown of each component.

The weights are as follows:

• Homework: 20%
• Quizzes: 10%
• Tests: 40%
• Final exam: 30%

Mariah's current scores are:

• Homework: 97.85%
• Quizzes: 92.05%
• Tests: 74.37%
• Final exam: not provided yet (let's call it $x$).

The formula for the weighted average is:

$\text{Overall Grade} = (\text{Homework score} \times 0.20) + (\text{Quiz score} \times 0.10) + (\text{Test score} \times 0.40) + (\text{Final Exam score} \times 0.30)$

Substituting the known values:

$\text{Overall Grade} = (97.85 \times 0.20) + (92.05 \times 0.10) + (74.37 \times 0.40) + (x \times 0.30)$

$\text{Overall Grade} = 19.57 + 9.21 + 29.75 + (x \times 0.30)$

$\text{Overall Grade} = 58.53 + (x \times 0.30)$

Now, her overall grade depends on her final exam score $x$.

Would you like me to solve for a specific final exam score, or explore how different exam scores might affect her overall grade?

---

Here are 5 questions that relate to this:

1. What score does Mariah need on the final exam to achieve a 90% overall grade?
2. What is the lowest score she can get on the final exam and still pass with a 70% overall?
3. How would the overall grade change if the quiz weight was higher than 10%?
4. What if her test average was 80% instead of 74.37%?
5. How would her overall grade be impacted if she didn’t take the final exam?

Tip: When calculating weighted averages, always ensure that the sum of the weights equals 100%.