Question: 105. The ratio of 12-year-olds to 13-year-olds in Mr. Wur's class is $5:3$. If there are $24$ students in the class, how many students are 13 years old?
1. **State the problem:** We are given the ratio of 12-year-olds to 13-year-olds as $5:3$ and the total number of students as $24$. We need to find how many students are 13 years old.
2. **Set up the ratio and total:** Let the number of 12-year-olds be $5x$ and the number of 13-year-olds be $3x$ because the ratio is $5:3$.
3. **Write the equation for total students:**
$$5x + 3x = 24$$
4. **Simplify the equation:**
$$8x = 24$$
5. **Solve for $x$:**
$$x = \frac{24}{8}$$
$$x = 3$$
6. **Find the number of 13-year-olds:**
$$3x = 3 \times 3 = 9$$
**Answer:** There are $9$ students who are 13 years old.