Solve the Weighted Average Puzzle: Determine the Missing Final Exam Grade

To solve this problem, we'll follow these steps:

• Step 1: Calculate the weighted score for each component.
• Step 2: Sum these scores and express the total weighted score needed for the average.
• Step 3: Solve for the unknown final exam grade using the weighted average formula.

Now, let's work through each step:

Step 1: Calculate the individual components' weighted scores:

• Attendance: $95 \times 0.10 = 9.5$
• Assessment: $82 \times 0.10 = 8.2$
• Assignments: $100 \times 0.20 = 20.0$

Step 2: Calculate the total weighted score needed to achieve an average of 92.

The weighted average formula is given by:

$\text{Weighted Average} = \sum (\text{Grade} \times \text{Weight}) = 92$ $(9.5 + 8.2 + 20.0 + \text{Final Exam Grade} \times 0.60) = 92$

Simplifying what we know:

$37.7 + \text{Final Exam Grade} \times 0.60 = 92$

Step 3: Solve for the final exam grade.

First, isolate the weighted exam score:

$\text{Final Exam Grade} \times 0.60 = 92 - 37.7 = 54.3$

Next, solve for the actual final exam grade:

$\text{Final Exam Grade} = \frac{54.3}{0.60} = 90.5$

Therefore, the grade the student received on the final exam is $90.5$.