Calculate Javier's Weighted Exam Score: Solve for x when 0.55x + 0.45(76) = 84

Q: Why do I need to convert percentages to decimals?

Percentages represent parts out of 100, but for calculations you need the actual decimal value. For example, 55% means 55/100 = 0.55. Using 55 instead of 0.55 makes your answer 100 times too big!

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

Use the formula: Final Average = (Weight₁ × Score₁) + (Weight₂ × Score₂). Make sure your weights add up to 1.0 (like 0.55 + 0.45 = 1.0).

Q: Can I solve this without converting to decimals?

Yes! You could write $ 84 = \frac{55}{100}x + \frac{45}{100}(76) $, but converting to decimals first makes the arithmetic much easier and reduces calculation errors.

Q: How do I check if my weighted average is correct?

Substitute your answer back: $ 0.55(90.55) + 0.45(76) = 49.8025 + 34.2 = 84 $. The result should equal the given final average!

Step-by-step video solution

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Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

How much does Javier score on the first exam that has a weight of 55%, given that he scores 76 on the second exam and his final average is 84?

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

Step 1: Define the weights and scores for each exam.
Step 2: Formulate the equation for the weighted average.
Step 3: Solve the equation for $x$ , the unknown score on the first exam.

Now, let's work through each step:

Step 1: We know:

Weight of the first exam: $0.55$
Weight of the second exam: $0.45$
Score on the second exam: $76$
Final average score: $84$
Unknown score (first exam): Let it be $x$

Step 2: We use the weighted average formula:

84 = 0.55 \times x + 0.45 \times 76

Step 3: Now solve for $x$ .

First, calculate the contribution of the second exam:

0.45 \times 76 = 34.2

Substitute this back into the equation:

84 = 0.55 \times x + 34.2

Subtract 34.2 from both sides to solve for $0.55 \times x$ :

84 - 34.2 = 0.55 \times x

49.8 = 0.55 \times x

Finally, divide both sides by 0.55 to isolate $x$ :

x = \frac{49.8}{0.55}

Calculate the result:

x \approx 90.55

Therefore, the solution to the problem is $\mathbf{90.55}$ .

3

Final Answer

$90.55$

Key Points to Remember

Essential concepts to master this topic

Weighted Average Formula: Final average equals sum of weighted individual scores
Technique: Convert percentages to decimals: 55% becomes 0.55 × x
Check: Substitute x = 90.55: 0.55(90.55) + 0.45(76) = 84 ✓

Common Mistakes

Avoid these frequent errors

Using percentages instead of decimals in calculations
Don't use 55% and 45% directly in equations = wrong scale! This gives answers 100 times larger than correct. Always convert percentages to decimals first: 55% = 0.55, 45% = 0.45.

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 do I need to convert percentages to decimals?

+

Percentages represent parts out of 100, but for calculations you need the actual decimal value. For example, 55% means 55/100 = 0.55. Using 55 instead of 0.55 makes your answer 100 times too big!

How do I set up a weighted average equation?

+

Use the formula: Final Average = (Weight₁ × Score₁) + (Weight₂ × Score₂). Make sure your weights add up to 1.0 (like 0.55 + 0.45 = 1.0).

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

+

Real weighted averages should always total 100% (or 1.0 in decimal form). If they don't, double-check the problem - there might be missing information or an error in the given weights.

Can I solve this without converting to decimals?

+

Yes! You could write $84 = \frac{55}{100}x + \frac{45}{100}(76)$ , but converting to decimals first makes the arithmetic much easier and reduces calculation errors.

How do I check if my weighted average is correct?

+

Substitute your answer back: $0.55(90.55) + 0.45(76) = 49.8025 + 34.2 = 84$ . The result should equal the given final average!

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Calculate Javier's Weighted Exam Score: Solve for x when 0.55x + 0.45(76) = 84

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