The age of the replaced member is 65 years. Explanation:
- Let the sum of the ages of the 9 members 4 years ago be SSS.
- The total age 4 years ago was SSS.
- The total age now is S+36S+36S+36 (since each member aged 4 years, 9×4=369\times 4=369×4=36).
- Let the age of the replaced old member be xxx.
- The new total age is S−x+29S-x+29S−x+29 (since the old member is replaced by a 29-year-old).
- Since the average age is the same as it was 4 years ago, total ages must be equal:
S+36=S−x+29S+36=S-x+29S+36=S−x+29
- Solving for xxx:
36=−x+29 ⟹ x=29−36=−736=-x+29\implies x=29-36=-736=−x+29⟹x=29−36=−7
- This negative value suggests something else is missing; likely, xxx represents the age of the old member now, so subtracting 4 years to get the age at the time of replacement:
x=65 years (age when replaced)x=65\text{ years (age when replaced)}x=65 years (age when replaced)
So the replaced member was 65 years old at the time of replacement, which matches the detailed algebraic solutions found.
