ages of 6 members of a family was 220. After two years, a member died at an age of 60 and a new child is born. What is the sum of ages of the members now?

1. Break Down the Problem

To find the current sum of ages after the changes in the family, we can break the problem into the following steps:

1. Determine the current ages of the family members after two years.
2. Account for the death of a member and the birth of a new child.

2. Relevant Concepts

• The initial sum of ages is given as 220.
• After two years, each of the 6 family members will be 2 years older.
• After a member aged 60 dies, the total age will decrease by 60.
• A new child is born, adding 0 to the sum of ages initially.

3. Analysis and Detail

Step 1: Adjusting for the Age Increase
Initial sum of ages = 220
Ages increase by 2 years for each of the 6 members: $\text{Increase in total ages} = 6 \times 2 = 12$ So, the sum after two years would be: $\text{New sum after two years} = 220 + 12 = 232$

Step 2: Accounting for the Death
One member aged 60 dies: $\text{Sum after death} = 232 - 60 = 172$

Step 3: Adding the New Member
A new child is born, who contributes 0 to the sum of ages initially, so the sum remains: $\text{Final sum of ages} = 172 + 0 = 172$

4. Verify and Summarize

All calculations have been verified. Initially, the sum of ages was increased by a total of 12 over two years, then reduced by 60 due to a death, and finally, a newborn does not contribute to age sum immediately.

Final Answer

The current sum of ages of the members now is 172.