Calculate Gabriel's Final Grade: Weighted Average with 30%, 15%, 35%, and 20% Contributions

Q: Why can't I just find the regular average of all four grades?

A regular average treats all grades equally, but weighted averages give different importance to each grade. Gabriel's project counts for 35% while his exam only counts for 15% - they shouldn't have equal impact!

Q: How do I convert percentages to decimals quickly?

Simply move the decimal point two places left: 30% becomes 0.30, 15% becomes 0.15. Or divide by 100: $ 30 \div 100 = 0.30 $

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

The weights must add up to 100% for a proper weighted average. If they don't, check the problem again or ask your teacher - there might be missing information or an error.

Q: Can I get a weighted average higher than my highest grade?

No! The weighted average will always fall between your lowest and highest grades. If you calculate something outside this range, you've made an error.

Q: Should I round my final answer?

Follow your teacher's instructions! Some want exact decimals, others want rounding to the nearest whole number. In this case, Gabriel's weighted average is exactly 85.

Weighted Averages with Percentage Calculations

A teacher wants to calculate Gabriel's final weighted average.

The following are Gabriel's exam results:

What is Gabriel's final average?

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Understand the problem

A teacher wants to calculate Gabriel's final weighted average.

The following are Gabriel's exam results:

What is Gabriel's final average?

Step-by-step solution

To calculate Gabriel's final weighted average, we'll use the formula for a weighted average:

$\text{Weighted Average} = (\text{Test 1 Grade} \times \text{Weight 1}) + (\text{Exam Grade} \times \text{Weight 2}) + (\text{Test 2 Grade} \times \text{Weight 3}) + (\text{Project Grade} \times \text{Weight 4})$

Next, calculate the contribution of each component:

Test 1 Contribution: $84 \times 0.30 = 25.2$
Exam Contribution: $73 \times 0.15 = 10.95$
Test 2 Contribution: $87 \times 0.35 = 30.45$
Project Contribution: $92 \times 0.20 = 18.4$

Now, add all these contributions to find the final weighted average:

$\text{Weighted Average} = 25.2 + 10.95 + 30.45 + 18.4 = 85$

Therefore, Gabriel's final weighted average is $\boxed{85}$ .

Final Answer

$85$

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply each grade by its weight, then add all products
Technique: Convert percentages to decimals: 30% becomes 0.30 for calculations
Check: All weights must sum to 100%: 30% + 15% + 35% + 20% = 100% ✓

Common Mistakes

Avoid these frequent errors

Adding grades first, then applying weights
Don't add 84 + 73 + 87 + 92 = 336, then multiply by weights = wrong calculation! This treats all grades equally instead of giving proper weight to each component. Always multiply each grade by its individual weight first, then add the weighted contributions.

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

Why can't I just find the regular average of all four grades?

A regular average treats all grades equally, but weighted averages give different importance to each grade. Gabriel's project counts for 35% while his exam only counts for 15% - they shouldn't have equal impact!

How do I convert percentages to decimals quickly?

Simply move the decimal point two places left: 30% becomes 0.30, 15% becomes 0.15. Or divide by 100: $30 \div 100 = 0.30$

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

The weights must add up to 100% for a proper weighted average. If they don't, check the problem again or ask your teacher - there might be missing information or an error.

Can I get a weighted average higher than my highest grade?

No! The weighted average will always fall between your lowest and highest grades. If you calculate something outside this range, you've made an error.

Should I round my final answer?

Follow your teacher's instructions! Some want exact decimals, others want rounding to the nearest whole number. In this case, Gabriel's weighted average is exactly 85.

How do I remember which grade gets which weight?

Make a simple table or list matching each assignment type with its weight. Double-check by ensuring the most important assignments (highest weights) have the biggest impact on your calculation.

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