We are given that the ratio of 12-year-olds to 13-year-olds is 5:3, and the total number of students in the class is 24. We need to determine how many students are 13 years old.

Step 1: Represent the number of students

Let the number of 12-year-olds be represented as $5x$ and the number of 13-year-olds as $3x$, where $x$ is the common factor in the ratio.

Step 2: Set up the equation for the total number of students

The total number of students is 24, so we have the equation:

$5x + 3x = 24$

Step 3: Solve for $x$

Combine the terms on the left-hand side:

$8x = 24$

Now, divide both sides by 8:

$x = 3$

Step 4: Calculate the number of 13-year-olds

The number of 13-year-olds is $3x$. Since $x = 3$:

$3x = 3 \times 3 = 9$

Thus, there are 9 students who are 13 years old.

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Do you need any further explanation or have additional questions about this problem?

Related questions:

1. If the ratio of 12-year-olds to 13-year-olds was 7:5, how many 13-year-olds would there be?
2. How would the number of 13-year-olds change if the total number of students increased to 30?
3. What if the ratio changed to 4:5, how would you calculate the number of 13-year-olds?
4. If there were only 20 students in the class, what would the number of 13-year-olds be with the original ratio?
5. How do you find the number of students in a class when given a ratio and the total number of students?

Tip:

When solving ratio problems, always express the quantities in terms of a common variable, as this will help set up a solvable equation.