Let the total number of students in the class be denoted by $x$.

Step 1: Express the number of girls and boys

• Girls: Since $\frac{5}{8}$ of the class is girls, the number of girls is $\frac{5}{8} \times x$.
• Boys: The rest of the students are boys. Since $\frac{5}{8}$ of the class is girls, the remaining fraction $1 - \frac{5}{8} = \frac{3}{8}$ of the class is boys. Therefore, the number of boys is $\frac{3}{8} \times x$.

Step 2: Use the given information about the number of girls

We are told that there are 12 more girls than boys. So, the difference between the number of girls and boys can be expressed as: $\frac{5}{8} \times x - \frac{3}{8} \times x = 12$ Simplifying: $\frac{2}{8} \times x = 12$ $\frac{1}{4} \times x = 12$

Step 3: Solve for $x$

To find $x$, multiply both sides of the equation by 4: $x = 12 \times 4$ $x = 48$

Conclusion:

The total number of students in the class is 48.

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Would you like more details on any step?

Here are some related questions you can explore:

1. If the number of girls was 3/4 of the class, how would the solution change?
2. How would the number of students in the class change if there were only 5 more girls than boys?
3. What is the ratio of girls to boys in the class?
4. If the total number of students was increased by 10, how would that affect the number of girls and boys?
5. How can we use algebra to model different real-life situations like this one?

Tip: Always remember to carefully analyze the fractions and their relation to the total amount when dealing with problems involving proportions.