Problem Analysis:
To find the age of the 10th child, we can use the concept of average and solve the problem step by step. We are given the average age of 10 children and the average age of 9 children. By finding the difference between these two averages, we can determine the age of the 10th child.

Solution:
Let's proceed with the solution step by step:

Step 1: Find the sum of ages of the 10 children.
- Average age of 10 children = 8 years 2 months
- To find the sum, we multiply the average by the number of children: (8 years + 2 months) × 10 = 82 years + 20 months.

Step 2: Find the sum of ages of the 9 children.
- Average age of 9 children = 8 years 8 months
- To find the sum, we multiply the average by the number of children: (8 years + 8 months) × 9 = 76 years + 72 months.

Step 3: Find the difference between the sum of ages of 10 children and the sum of ages of 9 children.
- Difference = (82 years + 20 months) - (76 years + 72 months) = 6 years + 48 months.

Step 4: Divide the difference by the number of children.
- To find the age of the 10th child, we divide the difference by 1 (since we are finding the age of a single child): (6 years + 48 months) ÷ 1 = 6 years + 48 months.

Step 5: Convert the months to years and months.
- Since 12 months make 1 year, we can convert the remaining months: 48 months ÷ 12 = 4 years.
- Therefore, the age of the 10th child is 6 years + 4 years = 10 years.

So, the age of the 10th child is 10 years.

Total age of 10 children equal 1170 months total age of 9 children equal 963 month