Reverse Percentage Problem: Finding Total Students from 80% Boys and 12 Girls

Q: How do I know which percentage to use in my equation?

Always match the percentage to the group you have numbers for! Since we know there are 12 girls, we use 20% (the percentage of girls), not 80%.

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

Calculate both groups: Boys: $ 0.80 \times 60 = 48 $Girls: $ 0.20 \times 60 = 12 $Total: 48 + 12 = 60 ✓

Q: What if the problem gave me the number of boys instead?

Then you'd use 80% in your equation! For example, if there were 48 boys, you'd write: $ 0.80 \times \text{Total} = 48 $

Percentage Problems with Unknown Totals

80% of the students in a class are boys, while the number of students who are girls is 12. How many students are there in total?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the total number of students in the class

00:05 The number of boys according to the data

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

00:15 This is the percentage of girls in the class

00:25 Construct an appropriate equation according to the data

00:30 Convert from a percentage to a fraction

00:35 Use the formula to convert percentages to fractions

00:40 Apply this formula to our exercise

00:50 Break down 100 into factors of 5 and 20

01:00 Reduce wherever possible

01:10 Isolate the total number of students

01:15 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

80% of the students in a class are boys, while the number of students who are girls is 12. How many students are there in total?

Step-by-step solution

To solve this problem, we'll first determine the percentage of students who are girls and then use it to find the total number of students.

1. Determine the percentage of students who are girls. Since 80% of the students are boys, it follows that 20% are girls.

2. We know that 20% of the total number of students is equal to 12 (the number of girls). We can set up the equation:

$0.20 \times \text{Total students} = 12$

3. Solve for the total number of students:

$\text{Total students} = \frac{12}{0.20}$

$\text{Total students} = 60$

Therefore, the total number of students in the class is $60$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Use complement percentages when one group is missing information
Technique: Set up equation $0.20 \times \text{Total} = 12$
Check: Verify 80% of 60 = 48 boys and 20% of 60 = 12 girls ✓

Common Mistakes

Avoid these frequent errors

Using 80% to calculate directly with 12 girls
Don't set up 0.80 × Total = 12 because 12 represents girls, not boys! This gives Total = 15, which is impossible since we'd need negative boys. Always match the percentage to the correct group - use 20% for girls.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction $\frac{75}{100}$

to a percentage:

FAQ

Everything you need to know about this question

How do I know which percentage to use in my equation?

Always match the percentage to the group you have numbers for! Since we know there are 12 girls, we use 20% (the percentage of girls), not 80%.

What if I don't know the percentage of girls directly?

No problem! Since percentages must add to 100%, you can find it: 100% - 80% = 20%. This is called the complement.

Can I solve this problem a different way?

Yes! You could also think: if 12 girls = 20% of total, then 1% = 0.6 students. So 100% = 0.6 × 100 = 60 students total.

How do I check if my answer makes sense?

Calculate both groups:

Boys: $0.80 \times 60 = 48$
Girls: $0.20 \times 60 = 12$

Total: 48 + 12 = 60 ✓

What if the problem gave me the number of boys instead?

Then you'd use 80% in your equation! For example, if there were 48 boys, you'd write: $0.80 \times \text{Total} = 48$

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