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

Q: Why don't I divide by the number of exams?

This is a weighted average, not a simple average! Each exam has different importance (weight), so you can't just add and divide by 4. You must use each exam's specific weight.

Q: What does the weighted average formula really mean?

It means: Final Average = (Grade₁ × Weight₁) + (Grade₂ × Weight₂) + ... + (GradeN × WeightN). Each grade contributes based on its importance (weight).

Q: How do I check if 78 is really correct?

Substitute back: $ 75(0.20) + 82(0.30) + 94(0.12) + 78(0.38) = 15 + 24.6 + 11.28 + 29.64 = 80.52 $ ✓

Weighted Average with Missing Grade

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?

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Understand the problem

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?

Step-by-step solution

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 $78$ .

Final Answer

$78$

Key Points to Remember

Essential concepts to master this topic

Rule: Sum all weights must equal 100% for valid weighted average
Technique: Calculate known contributions: $75(0.20) + 82(0.30) + 94(0.12) = 50.88$
Check: Verify $50.88 + 78(0.38) = 80.52$ equals target average ✓

Common Mistakes

Avoid these frequent errors

Adding percentages instead of using decimal weights
Don't use 20% directly in calculations = wrong result of 1610.4! Percentages in calculations give inflated numbers. Always convert percentages to decimals first (20% = 0.20).

Practice Quiz

Test your knowledge with interactive questions

Norbert buys some new clothes.

When he gets home, he decides to work out how much each outfit cost him on average.

What answer should he come up with?

FAQ

Everything you need to know about this question

How do I find the weight of the missing exam?

Add up all the given weights: 20% + 30% + 12% = 62%. The missing weight is 100% - 62% = 38%. All weights must total exactly 100%!

Why don't I divide by the number of exams?

This is a weighted average, not a simple average! Each exam has different importance (weight), so you can't just add and divide by 4. You must use each exam's specific weight.

What if my calculated grade seems too high or too low?

Check your math! Common errors include using percentages instead of decimals (0.20 not 20) or forgetting to convert the final average correctly. Always verify by plugging your answer back in.

Can I solve this without finding the missing weight?

No, you need all weights to set up the equation correctly. The missing weight is crucial - it tells you how much the unknown exam contributes to the final average.

What does the weighted average formula really mean?

It means: Final Average = (Grade₁ × Weight₁) + (Grade₂ × Weight₂) + ... + (GradeN × WeightN). Each grade contributes based on its importance (weight).

How do I check if 78 is really correct?

Substitute back: $75(0.20) + 82(0.30) + 94(0.12) + 78(0.38) = 15 + 24.6 + 11.28 + 29.64 = 80.52$ ✓

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