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

Matt receives the following grades in his math exams:



If Matt's average is $80.52$, then what grade did he get on his last exam?

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 $78$.