Calculate Girls in Class: 70% of 40 Students are Boys

Q: Why can't I just calculate 30% of 40 directly?

You absolutely can! But first you need to recognize that girls make up 30% of the class. Since boys are 70%, girls must be 100% - 70% = 30%. Then calculate 30% of 40 = 12.

Q: Is there a faster way than calculating boys first?

Yes! Once you know girls are 30% of the class, you can calculate directly: $ \frac{30}{100} \times 40 = 12 $ girls. Both methods give the same answer!

Q: How do I check my answer is correct?

Add your results together! 28 boys + 12 girls = 40 total students. Also verify the percentages: $ \frac{28}{40} = 0.70 = 70\% $ boys ✓

Q: Do I always subtract the given percentage from 100%?

When dealing with complementary categories (like boys and girls), yes! The two groups must add up to 100% of the total. So if one group is 70%, the other is automatically 30%.

Percentage Problems with Complementary Categories

A class comprises 40 students, 70% of whom are boys. How many girls are there in the class?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the number of girls in the class

00:05 The percentage of boys according to the given data

00:10 We want to establish the percentage of girls

00:15 Subtract the percentage of boys from the whole in order to determine the percentage of girls

00:20 This is the percentage of girls in the class

00:25 Convert from a percentage to a fraction

00:30 Use the formula to convert percentages to fractions

00:35 Apply this formula to our exercise

00:40 Multiply this fraction by the whole in order to determine the number of girls in the class

00:50 Factor 30 into factors of 3 and 10, and 40 into factors of 4 and 10

00:55 Factor 100 into factors of 10 and 10

01:05 Simplify wherever possible

01:13 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A class comprises 40 students, 70% of whom are boys. How many girls are there in the class?

Step-by-step solution

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

Step 1: Calculate the number of boys in the class using the percentage given.
Step 2: Subtract the number of boys from the total number of students to determine the number of girls.

Now, let's work through each step:
Step 1: Calculate the number of boys.
The percentage of boys in the class is given as 70%. Thus, we calculate the number of boys as follows:

$\text{Number of boys} = \frac{70}{100} \times 40 = 28$

Step 2: Calculate the number of girls.
Since there are 40 students in total, the number of girls can be found by subtracting the number of boys from the total number of students:

$\text{Number of girls} = 40 - 28 = 12$

Therefore, the solution to the problem is $12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Find remaining percentage by subtracting from 100%
Technique: Calculate 70% of 40 = 28 boys, then 40 - 28 = 12 girls
Check: Verify 28 boys + 12 girls = 40 total students ✓

Common Mistakes

Avoid these frequent errors

Finding percentage of girls directly without converting
Don't calculate 30% of 40 = 12 without first recognizing that girls are 30%! Students often jump to the calculation without identifying that if 70% are boys, then 30% must be girls. Always find the complementary percentage first: 100% - 70% = 30%, then calculate 30% of 40.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just calculate 30% of 40 directly?

You absolutely can! But first you need to recognize that girls make up 30% of the class. Since boys are 70%, girls must be 100% - 70% = 30%. Then calculate 30% of 40 = 12.

Is there a faster way than calculating boys first?

Yes! Once you know girls are 30% of the class, you can calculate directly: $\frac{30}{100} \times 40 = 12$ girls. Both methods give the same answer!

What if the percentage doesn't come out to a whole number?

In real problems, you might get decimal answers like 12.5 students. For word problems, check if the context makes sense - you usually can't have half a student in a class!

How do I check my answer is correct?

Add your results together! 28 boys + 12 girls = 40 total students. Also verify the percentages: $\frac{28}{40} = 0.70 = 70\%$ boys ✓

Do I always subtract the given percentage from 100%?

When dealing with complementary categories (like boys and girls), yes! The two groups must add up to 100% of the total. So if one group is 70%, the other is automatically 30%.

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