Ramiro applies to a high school where the average grade required for mathematics is 85.The following are Ramiro's grades on his maths exams:GradeWeight40%15%10%35%92789883Will Ramiro be admitted to the high school and what is his grade average?

No, he has an average lower than 85.

Determine Ramiro's Mathematics Weighted Average: Will He Meet the 85 Requirement?

Q: Why can't I just add up all the grades and divide by 4?

That would give you a simple average, but this problem uses different weights for each grade! A 40% weight means that grade counts much more than a 10% weight grade.

Q: How do I convert percentages to decimals?

Simply divide by 100 or move the decimal point two places left. For example: 40% = 40 ÷ 100 = 0.40, and 15% = 0.15.

Q: Do the weights always need to add up to 100%?

Yes! In a proper weighted average, all weights must total exactly 100% (or 1.0 as decimals). Check: 40% + 15% + 10% + 35% = 100% ✓

Q: What if Ramiro's weighted average was exactly 85?

If the weighted average equals exactly 85, he would meet the requirement! The problem asks for an average of 85 or higher for admission.

Weighted Averages with Percentage Weights

Ramiro applies to a high school where the average grade required for mathematics is 85.

The following are Ramiro's grades on his maths exams:

Will Ramiro be admitted to the high school and what is his grade average?

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Step-by-step solution

To determine if Ramiro's grades meet the average required, we calculate the weighted average of his grades. This involves applying the formula for calculating a weighted average:

Multiply each grade by its corresponding weight:
$92 \times 0.40 = 36.8$
$78 \times 0.15 = 11.7$
$98 \times 0.10 = 9.8$
$83 \times 0.35 = 29.05$
Sum these products to calculate the weighted average:
$\text{Weighted Average} = 36.8 + 11.7 + 9.8 + 29.05 = 87.35$

Since 87.35 is greater than the required 85, Ramiro's weighted average meets the high school requirement.

Therefore, the solution to the problem is that Ramiro will be admitted to the high school. His weighted grade average is $87.35$ .

Final Answer

Yes, $87.35$

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply each grade by its weight percentage as decimal
Calculation: $92 \times 0.40 + 78 \times 0.15 + 98 \times 0.10 + 83 \times 0.35$
Verification: Check that all weights sum to 100% before calculating ✓

Common Mistakes

Avoid these frequent errors

Using percentages instead of decimals in calculations
Don't multiply grades by percentages like 92 × 40 = 3,680! This gives unrealistically high results because you're not converting percentages to decimals. Always convert percentages to decimals first: 40% becomes 0.40.

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 add up all the grades and divide by 4?

That would give you a simple average, but this problem uses different weights for each grade! A 40% weight means that grade counts much more than a 10% weight grade.

How do I convert percentages to decimals?

Simply divide by 100 or move the decimal point two places left. For example: 40% = 40 ÷ 100 = 0.40, and 15% = 0.15.

Do the weights always need to add up to 100%?

Yes! In a proper weighted average, all weights must total exactly 100% (or 1.0 as decimals). Check: 40% + 15% + 10% + 35% = 100% ✓

What if Ramiro's weighted average was exactly 85?

If the weighted average equals exactly 85, he would meet the requirement! The problem asks for an average of 85 or higher for admission.

Can I calculate this in a different order?

Absolutely! You can multiply and add in any order due to the commutative property. Just make sure each grade gets multiplied by its correct weight.

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