Calculate 30% Girls in 240 Students: Finding Boys in Summer Camp

Q: Why can't I just calculate 70% of 240 directly?

You absolutely can! Since 30% are girls, then 70% must be boys. Both methods work: $ 240 \times 0.70 = 168 $ or $ 240 - 72 = 168 $.

Q: How do I convert 30% to a decimal?

Divide the percentage by 100: 30 ÷ 100 = 0.30. You can also move the decimal point two places left: 30.0% becomes 0.30.

Q: How do I check if my answer makes sense?

Ask yourself: Does 168 boys + 72 girls = 240 total? Also, are there more boys than girls since only 30% are girls? Both should be true!

Q: Can I solve this problem a different way?

Yes! You could find boys directly: Boys = 70% of 240. Or use algebra: Let G = girls, then $ G = 0.30 \times 240 $, so Boys = $ 240 - G $.

Percentage Problems with Complementary Groups

The number of students in the 7th grade camp is 240. 30% of the students are girls. Calculate the number of boys participating in the summer camp.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the number of boys participating in the summer camp

00:05 Determine the percentage of boys

00:10 Subtract the percentage of girls from the whole in order to calculate this percentage

00:24 Convert the percentage to a fraction

00:29 Use the formula to convert percentages to fractions

00:34 Apply this formula to our exercise

00:42 Multiply this fraction by the number of students in order to establish the number of boys

00:47 Factor 70 into 7 and 10, and 100 into 10 and 10

00:55 Factor 240 into 24 and 10

01:02 Reduce wherever possible

01:17 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The number of students in the 7th grade camp is 240. 30% of the students are girls. Calculate the number of boys participating in the summer camp.

Step-by-step solution

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

Step 1: Calculate the number of girls using the percentage provided.
Step 2: Deduct the number of girls from the total number of students to find the number of boys.

Now, let's work through each step:
Step 1: The percentage of students that are girls is 30%. So, we find the number of girls by calculating:

\text{Number of Girls} = 240 \times \left(\frac{30}{100}\right)

Calculating this gives:

\text{Number of Girls} = 240 \times 0.30 = 72

Step 2: Subtract the number of girls from the total number of students to find the number of boys:
Number of Boys = Total Students - Number of Girls = 240 - 72 = 168

Therefore, the number of boys participating in the summer camp is $168$ .

Final Answer

168

Key Points to Remember

Essential concepts to master this topic

Rule: Girls percentage + Boys percentage = 100%
Technique: Calculate girls first: $240 \times 0.30 = 72$ girls
Check: Verify boys + girls equals total: 168 + 72 = 240 ✓

Common Mistakes

Avoid these frequent errors

Calculating boys percentage directly instead of girls first
Don't try to find 70% of 240 directly without calculating girls first = confusion about which percentage to use! Many students mix up the given percentage with the one they need to find. Always calculate the given percentage first (30% girls = 72), then subtract from total.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just calculate 70% of 240 directly?

You absolutely can! Since 30% are girls, then 70% must be boys. Both methods work: $240 \times 0.70 = 168$ or $240 - 72 = 168$ .

How do I convert 30% to a decimal?

Divide the percentage by 100: 30 ÷ 100 = 0.30. You can also move the decimal point two places left: 30.0% becomes 0.30.

What if the percentage doesn't give a whole number?

That's fine! Real-world problems often have decimal answers. Just make sure to round appropriately - you can't have 72.5 students!

How do I check if my answer makes sense?

Ask yourself: Does 168 boys + 72 girls = 240 total? Also, are there more boys than girls since only 30% are girls? Both should be true!

Can I solve this problem a different way?

Yes! You could find boys directly: Boys = 70% of 240. Or use algebra: Let G = girls, then $G = 0.30 \times 240$ , so Boys = $240 - G$ .

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