Calculate Monica's Weighted Average: Grades from 30% and 70% Inputs

Q: Why can't I just average 98 and 95 to get 96.5?

Because the exam is worth 70% while the assignment is only 30%! A simple average treats them equally, but the exam should have more influence on Monica's final grade since it's worth more.

Q: How do I convert percentages to decimals?

Divide by 100 or move the decimal point two places left: 30% = 30 ÷ 100 = 0.30 and 70% = 70 ÷ 100 = 0.70.

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

The weights must always total 100% for a complete grade calculation. If they don't, check the problem statement again or ask your teacher for clarification.

Q: Should my weighted average be between the two grades?

Yes! Your weighted average should fall between 95 and 98. Since 95.9 is between these values, we know our answer makes sense.

Q: Can I do this calculation in a different order?

Yes! You can calculate $ 95 \times 0.70 + 98 \times 0.30 $ instead. The order doesn't matter as long as you multiply each grade by its correct weight.

Q: What does the weighted average tell me?

It shows Monica's overall performance accounting for how much each assignment matters. Since the exam (95) is worth more, it pulls the average closer to 95 than to 98.

Weighted Averages with Percentage Weights

What is Monica's average grade if she gets 98 on an assignment that represents 30% and a 95 on an exam that represents 70%?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is Monica's average grade if she gets 98 on an assignment that represents 30% and a 95 on an exam that represents 70%?

Step-by-step solution

Let's solve the problem by applying the steps we outlined:

Step 1: Identify the grade and weight for each component:
- Assignment: Grade = 98, Weight = 30% (or 0.30)
- Exam: Grade = 95, Weight = 70% (or 0.70)
Step 2: Apply the weighted average formula:
- Compute the weighted grade for each component:
Weighted grade for assignment = $98 \times 0.30 = 29.4$
Weighted grade for exam = $95 \times 0.70 = 66.5$
Step 3: Sum the weighted grades to find Monica's average grade:
- Total weighted average = $29.4 + 66.5 = 95.9$

Therefore, Monica's average grade is $95.9$ .

Final Answer

$95.9$

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply each grade by its weight, then sum products
Technique: Convert percentages to decimals: 30% = 0.30, 70% = 0.70
Check: Weights must sum to 100% and result should be reasonable ✓

Common Mistakes

Avoid these frequent errors

Using simple average instead of weighted average
Don't add grades and divide by 2: (98 + 95) ÷ 2 = 96.5, which ignores the weights! This treats both components equally when the exam is worth more than twice the assignment. Always multiply each grade by its weight first, then sum the products.

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 average 98 and 95 to get 96.5?

Because the exam is worth 70% while the assignment is only 30%! A simple average treats them equally, but the exam should have more influence on Monica's final grade since it's worth more.

How do I convert percentages to decimals?

Divide by 100 or move the decimal point two places left: 30% = 30 ÷ 100 = 0.30 and 70% = 70 ÷ 100 = 0.70.

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

The weights must always total 100% for a complete grade calculation. If they don't, check the problem statement again or ask your teacher for clarification.

Should my weighted average be between the two grades?

Yes! Your weighted average should fall between 95 and 98. Since 95.9 is between these values, we know our answer makes sense.

Can I do this calculation in a different order?

Yes! You can calculate $95 \times 0.70 + 98 \times 0.30$ instead. The order doesn't matter as long as you multiply each grade by its correct weight.

What does the weighted average tell me?

It shows Monica's overall performance accounting for how much each assignment matters. Since the exam (95) is worth more, it pulls the average closer to 95 than to 98.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Weighted Average questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime