The problem is to find the value of $n$ such that the average of the numbers $3, 4, 9,$ and $n$ equals $24$.

Step-by-Step Solution:

1. Recall the formula for the average: $\text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of terms}}$

2. Substitute the given values into the formula: $24 = \frac{3 + 4 + 9 + n}{4}$

3. Simplify the numerator: $24 = \frac{16 + n}{4}$

4. Eliminate the fraction by multiplying through by $4$: $96 = 16 + n$

5. Solve for $n$: $n = 96 - 16 = 80$

Final Answer:

The value of $n$ is $\mathbf{80}$.

---

Would you like further clarification or additional examples?

Related Questions:

1. How do you calculate the average when more numbers are added?
2. What happens if $n$ is negative in similar problems?
3. How does the formula for weighted averages differ from simple averages?
4. Can the average of integers be a non-integer? Provide examples.
5. What is the sum of $n$ consecutive integers if their average is given?

Tip:

Always double-check your calculations when dealing with averages by recalculating the total sum and verifying the division.