Calculate Class Size: Finding Total Students with Scores 85 and 92 Using Mean of 88.5

Q: Why can't I find just one answer for the number of students?

Great question! When you set up the equation, the variable n cancels out completely. This means the average of 88.5 will be true for any even number of students - 2, 4, 100, or 1000!

Q: How do I know the number of students must be even?

Since half the students score 85 and half score 92, you need to be able to split the class into two equal groups. This is only possible with an even number of students.

Q: What if the problem asked for students scoring different amounts?

If the scores or proportions changed, you'd likely get a specific answer for n. The key here is that 88.5 is exactly halfway between 85 and 92, making any even class size work.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

In an exam, half of the students score 85 and the other half score 92. The average score on the test was 88.5.

How many students are in the class?

2

Step-by-step solution

To solve this problem, we'll first set up an equation representing the given situation:

Let $n$ represent the total number of students.
The number of students scoring 85 is $\frac{n}{2}$ , and the number scoring 92 is also $\frac{n}{2}$ .
The total sum of all scores is $\frac{n}{2} \times 85 + \frac{n}{2} \times 92$ .
Given that the average score is 88.5, set up the equation:

\frac{\frac{n}{2} \times 85 + \frac{n}{2} \times 92}{n} = 88.5

Simplify and solve the equation:

First, calculate the total score:

\frac{n}{2} \times 85 + \frac{n}{2} \times 92 = \frac{n}{2} (85 + 92)

$= \frac{n}{2} \times 177 = 88.5 \times n$

Now, set up the equation:

\frac{n \times 177}{2} = 88.5 \times n

Cancel $n$ from both sides (assuming $n \neq 0$ ):

\frac{177}{2} = 88.5

The equation is inherently true, and $n$ cancels out, showing that $n$ could be any even and positive integer to satisfy the given conditions.

Therefore, the number of students in the class could be any even and positive integers.

3

Final Answer

The number of students in the class could be any even and positive integers.

Key Points to Remember

Essential concepts to master this topic

Setup: Half students score 85, half score 92, average is 88.5
Technique: $\frac{n}{2} \times 85 + \frac{n}{2} \times 92 = n \times 88.5$
Check: Simplify to verify $\frac{177}{2} = 88.5$ is always true ✓

Common Mistakes

Avoid these frequent errors

Trying to solve for a specific number of students
Don't assume there's one unique answer and try solving n = some number! This leads to confusion because n cancels out completely. Always recognize when an equation is satisfied by any value that meets the given constraints (any even positive integer).

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why can't I find just one answer for the number of students?

+

Great question! When you set up the equation, the variable n cancels out completely. This means the average of 88.5 will be true for any even number of students - 2, 4, 100, or 1000!

How do I know the number of students must be even?

+

Since half the students score 85 and half score 92, you need to be able to split the class into two equal groups. This is only possible with an even number of students.

Can I check this with a specific example?

+

Absolutely! Try 10 students: 5 score 85, 5 score 92. Total points = $5 \times 85 + 5 \times 92 = 425 + 460 = 885$ . Average = $\frac{885}{10} = 88.5$ ✓

What if the problem asked for students scoring different amounts?

+

If the scores or proportions changed, you'd likely get a specific answer for n. The key here is that 88.5 is exactly halfway between 85 and 92, making any even class size work.

Is this type of problem common in real life?

+

Yes! This shows an important concept: sometimes mathematical constraints are flexible rather than giving unique answers. It's like saying 'any recipe that uses equal amounts of two ingredients will have their average properties.'

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Calculate Class Size: Finding Total Students with Scores 85 and 92 Using Mean of 88.5

Average Calculation with Variable Constraints

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Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I find just one answer for the number of students?

How do I know the number of students must be even?

Can I check this with a specific example?

What if the problem asked for students scoring different amounts?

Is this type of problem common in real life?

🌟 Unlock Your Math Potential

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