Solve for Matt’s Final Exam: Completing His Weighted Grade Average of 80.52

To solve this problem, we need to calculate the grade Matt received on his last exam using the weighted average formula:

• Step 1: Calculate the contribution of the known grades.
• Step 2: Use the weighted average formula to solve for the unknown grade.
• Step 3: Perform the necessary calculations to determine the grade.

Let's calculate this step by step:
Step 1: Calculate the known parts of the weighted total:
$(75 \times 0.20) + (82 \times 0.30) + (94 \times 0.12) = 15 + 24.6 + 11.28 = 50.88$ Step 2: Let $x$ be the grade for the last exam. Since the weight for the last exam is 38%, the equation becomes:
$80.52 = \frac{50.88 + (x \times 0.38)}{1}$ Step 3: Solve for $x$:
$80.52 = 50.88 + 0.38x$ $0.38x = 80.52 - 50.88 = 29.64$ $x = \frac{29.64}{0.38} = 78$

Therefore, the grade Matt received on his last exam is $78$.