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

Q: Why can't I just average all the grades normally?

Because each component has different importance! The final exam is worth 60% of the grade, while attendance is only 10%. A weighted average accounts for these differences in importance.

Q: How do I set up the weighted average equation?

Use this format: $ \text{Grade}_1 \times \text{Weight}_1 + \text{Grade}_2 \times \text{Weight}_2 + ... = \text{Final Average} $Replace the unknown grade with a variable like x and solve!

Q: What if the weights don't add up to 100%?

Check your problem again! In a proper weighted average, all weights must total exactly 100% (or 1.0 as decimals). If they don't, there might be missing information.

Step-by-step video solution

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Step-by-step written solution

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1

Understand the problem

A teacher loses the final exam results of one of his students. Luckily for him, he had already calculated the student's average grade for this year.

If the student's average is 92, then what grade did he get on his final exam?

2

Step-by-step solution

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 $90.5$ .

3

Final Answer

90.5

Key Points to Remember

Essential concepts to master this topic

Formula: Total weighted score equals sum of all weighted components
Technique: Calculate known weights: 95(0.10) + 82(0.10) + 100(0.20) = 37.7
Check: Verify 90.5(0.60) + 37.7 = 54.3 + 37.7 = 92 ✓

Common Mistakes

Avoid these frequent errors

Using simple average instead of weighted average
Don't add all grades and divide by 4 = wrong answer! This ignores the importance of weights - the final exam counts for 60% while attendance is only 10%. Always multiply each grade by its weight percentage first.

Practice Quiz

Test your knowledge with interactive questions

A hotel's overall rating is determined according to a weighted average of several categories. Each category is given a rating and a weighted factor. Below are the ratings for the "Happy Tourist" hotel:

Determine the hotel's overall rating?

FAQ

Everything you need to know about this question

Why can't I just average all the grades normally?

+

Because each component has different importance! The final exam is worth 60% of the grade, while attendance is only 10%. A weighted average accounts for these differences in importance.

How do I set up the weighted average equation?

+

Use this format: $\text{Grade}_1 \times \text{Weight}_1 + \text{Grade}_2 \times \text{Weight}_2 + ... = \text{Final Average}$

Replace the unknown grade with a variable like x and solve!

What if the weights don't add up to 100%?

+

Check your problem again! In a proper weighted average, all weights must total exactly 100% (or 1.0 as decimals). If they don't, there might be missing information.

Can the missing grade be higher than 100?

+

Yes! If the other grades are low and you need a high average, the missing component might exceed 100. However, check if your problem has realistic constraints (like maximum possible scores).

How do I check if my answer makes sense?

+

Substitute your answer back into the weighted average formula. Also, consider: Is this grade reasonable? If you calculated 150 for a test, but the maximum is 100, recheck your work!

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

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