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

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

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1

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?

2

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

3. Solve for the total number of students:

Total students=120.20 \text{Total students} = \frac{12}{0.20}

Total students=60 \text{Total students} = 60

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

3

Final Answer

60

Practice Quiz

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Convert the fraction into a percentage:

\( \frac{2}{100}=\text{?} \)

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