Solving the Family Age Puzzle

This problem requires calculating the specific ages of the father and mother when the brother was born, using the provided age differences and birth events.

Key Age Relationships

• Brother's Age vs. Your Age: The brother is 4 years older. If your age is $A_{You}$, the brother's age $A_{Bro}$ is $A_{Bro} = A_{You} + 4$.
• Sister's Age vs. Brother's Age: The sister was 5 years old when the brother was born. This means the sister is 5 years older than the brother. $A_{Sis} = A_{Bro} + 5$.
• Father's Age at Sister's Birth: Father was 24 years old when $A_{Sis} = 0$.
• Mother's Age at Your Birth: Mother was 27 years old when $A_{You} = 0$.

Calculating Father's Age When Brother Was Born

We need the father's age when $A_{Bro} = 0$.

1. From $A_{Sis} = A_{Bro} + 5$, when the brother was born ($A_{Bro} = 0$), the sister's age was $A_{Sis} = 0 + 5 = 5$.
2. The father was 24 when the sister was born ($A_{Sis}=0$).
3. The brother was born 5 years *before* the sister ($A_{Bro} = A_{Sis} - 5$).
4. Therefore, when the brother was born, the father's age was his age at the sister's birth plus those 5 years: $24 + 5 = 29$ years.

Calculating Mother's Age When Brother Was Born

We need the mother's age when $A_{Bro} = 0$.

1. From $A_{Bro} = A_{You} + 4$, when the brother was born ($A_{Bro} = 0$), your age was $A_{You} = 0 - 4 = -4$. This means you were not yet born.
2. The mother was 27 years old when you were born ($A_{You}=0$).
3. Since your age was -4 when the brother was born, the mother's age at that time was $27 - 4 = 23$ years.

Conclusion

When the brother was born:

• Father's age was 29 years.
• Mother's age was 23 years.

The respective ages are 29 and 23.