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

Question

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?

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

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 $60$ .