Understanding the Age Puzzle
Introduction
Dr. Johnson inquired about his friend’s son’s age, leading to a complex age-related riddle.
Age Relationships
His friend provided the following relationships:
– His son is five times as old as his daughter.
– His wife is five times as old as his son.
– He is twice as old as his wife.
– His grandmother, who is celebrating her eighty-first birthday, is as old as the combined ages of the entire family.
Setting Up the Equations
Let:
– S = son’s age
– D = daughter’s age
– W = wife’s age
– F = friend’s age
From the information given, we can establish the following equations:
1. S = 5D
2. W = 5S = 25D
3. F = 2W = 50D
Additionally, we know that:
81 = D + S + W + F
Solving the Equations
Substituting the equations into the total age equation gives:
81 = D + 5D + 25D + 50D
This simplifies to:
81 = 81D
Dividing both sides by 81 results in:
D = 1
Now, substituting back to find S:
S = 5D = 5 * 1 = 5
Conclusion
Thus, Dr. Johnson’s friend’s son is five years old.