Question: The ratio of boys and girls is $5 : 7$. If there are $84$ students, how many are girls?
1. **State the problem:** We are given the ratio of boys to girls as $5 : 7$ and the total number of students as $84$. We need to find the number of girls.
2. **Formula and rules:** The total parts in the ratio = $5 + 7 = 12$ parts.
3. **Calculate the value of one part:**
$$\text{One part} = \frac{84}{12}$$
4. **Simplify the fraction:**
$$\frac{\cancel{84}}{\cancel{12}} = 7$$
5. **Calculate the number of girls:**
$$7 \times 7 = 49$$
6. **Answer:** There are $49$ girls in the class.