The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
👥 Age Proportion Puzzle 👥
Let’s break it down step by step:
Present ages are in proportion 4:7:9. Let’s assume the common multiplier is x:
Person 1’s age = 4x
Person 2’s age = 7x
Person 3’s age = 9x
Eight years ago, their ages were:
Person 1’s age = 4x – 8
Person 2’s age = 7x – 8
Person 3’s age = 9x – 8
The sum of their ages eight years ago was 56:
(4x – 8) + (7x – 8) + (9x – 8) = 56
Combine like terms:
20x – 24 = 56
Add 24 to both sides:
20x = 80
Divide by 20:
x = 4
Now, find their present ages:
Person 1’s age = 4x = 4 × 4 = 16
Person 2’s age = 7x = 7 × 4 = 28
Person 3’s age = 9x = 9 × 4 = 36
🎉 The present ages of the three persons are 16, 28, and 36 years. 👥
