The median of 10 numbers is 22. Find the tenth number given that 9 of the numbers are 39, 7, 44, 10. 14, 16, 24, 35, and 29.

Answer

To find the tenth number given that the median of 10 numbers is 22 and the first 9 numbers are 39, 7, 44, 10, 14, 16, 24, 35, and 29, we can follow these steps:

### Step-by-Step Solution:

1. **List the Given Numbers**: We have the following 9 numbers:
- 39, 7, 44, 10, 14, 16, 24, 35, 29

2. **Sort the Numbers in Ascending Order**: To find the median, we need to sort these numbers:
- Sorted order: 7, 10, 14, 16, 24, 29, 35, 39, 44

3. **Identify the Median Position**: Since we have 10 numbers, the median will be the average of the 5th and 6th numbers in the sorted list.
- The median is given as 22.

4. **Let the 10th Number be X**: We will denote the 10th number as X. After including X, the sorted list will still need to maintain the median of 22.

5. **Determine the Position of X**: The number X must be placed in such a way that the 5th and 6th numbers in the sorted list average to 22.
- The current 5th number is 24, and the 6th number will depend on where X is placed.

6. **Insert X into the Sorted List**: Depending on the value of X, we can have different placements:
- If X is less than 24, it will take the position of the 5th number, and the 6th number will be 24.
- If X is greater than or equal to 24, it will take the position after 24.

7. **Set Up the Equation for the Median**:
- If X is less than 24:
\[ \text{Median} = \frac{X + 24}{2} = 22 \]
- If X is greater than or equal to 24:
\[ \text{Median} = \frac{24 + \text{next number}}{2} = 22 \]
- Since we know the 6th number is 24, we can focus on the first case.

8. **Solve for X**:
- From the equation:
\[ X + 24 = 44 \implies X = 20 \]

9. **Conclusion**: The 10th number is:
- X = 20

10. **Final Sorted List**: The complete sorted list of numbers is:
- 7, 10, 14, 16, 20, 24, 29, 35, 39, 44

### Final Answer:
The tenth number is **20**.