Calculate Student Height Percentages: Finding Statistics in a School of 160 Students

Q: Why can't I just use the 32 students in Silvana's class?

The question asks about all students in her school, not just her class! You need the total population of 160 students (5 classes × 32 students each) to get the correct percentage.

Q: What if Silvana is exactly the same height as some students?

The problem asks for students shorter than Silvana. If some students are the same height, they wouldn't count as shorter. But since we're told exactly 40 are taller, the remaining 120 students are shorter.

Q: Can I solve this without finding the total number of students?

No! You need the total population as your denominator in the percentage formula. Without knowing there are 160 total students, you can't calculate what fraction 40 represents.

Q: How do I check if my percentage calculation is correct?

Use the percentage formula: $ \frac{\text{part}}{\text{whole}} \times 100\% $. Check: $ \frac{120}{160} \times 100\% = 75\% $ ✓

Percentage Calculations with Population Analysis

Silvana checks approximately what percentage of students in her school are shorter than her.

There are 32 students in Silvana's class. There are a total of 5 equally sized classes in the school and 40 students in the school are taller than her.

What is the answer to Silvana's question?

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Step-by-step written solution

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Understand the problem

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the total number of students in the school.
Step 2: Calculate the percentage of students who are taller than Silvana.

Now, let's work through each step:
Step 1: Silvana's school has 5 classes, each with 32 students. To find the total number of students, we multiply the number of classes by the number of students per class:
$5 \times 32 = 160 \text{ students}$ .

Step 2: We know 40 students are taller than Silvana. We use the percentage formula to find the percentage of students taller than Silvana:
$\frac{40}{160} \times 100\% = 25\%$ .

Therefore, the answer to Silvana's question is 25%.

Final Answer

75%

Key Points to Remember

Essential concepts to master this topic

Total Population: Multiply number of groups by group size first
Technique: Calculate known percentage first: $\frac{40}{160} \times 100\% = 25\%$
Check: All percentages should sum to 100%: 25% + 75% = 100% ✓

Common Mistakes

Avoid these frequent errors

Finding percentage of students shorter without calculating total population first
Don't try to find the percentage using just one class size = wrong denominator! This gives 40/32 which is over 100%. Always calculate total population first: 5 × 32 = 160 students.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{6}{25}$ as a percentage?

FAQ

Everything you need to know about this question

Why can't I just use the 32 students in Silvana's class?

The question asks about all students in her school, not just her class! You need the total population of 160 students (5 classes × 32 students each) to get the correct percentage.

How do I know if 40 students taller means 75% are shorter?

If 40 out of 160 students are taller, that's 25% taller. Since percentages must add to 100%, the remaining students (100% - 25% = 75%) must be shorter than or equal to Silvana's height.

What if Silvana is exactly the same height as some students?

The problem asks for students shorter than Silvana. If some students are the same height, they wouldn't count as shorter. But since we're told exactly 40 are taller, the remaining 120 students are shorter.

Can I solve this without finding the total number of students?

No! You need the total population as your denominator in the percentage formula. Without knowing there are 160 total students, you can't calculate what fraction 40 represents.

How do I check if my percentage calculation is correct?

Use the percentage formula: $\frac{\text{part}}{\text{whole}} \times 100\%$ . Check: $\frac{120}{160} \times 100\% = 75\%$ ✓

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