Algebra Puzzle: "Digits of age interchanged, 1 added, answer half present age" – Solution

Let Alberta's age be a two-digit number: 10a + b (where a = tens digit, b = units digit).

Given

Interchange digits → 10b + a
Add 1 → 10b + a + 1
This equals half her present age → (10a + b)/2

Equation

10b + a + 1 = (10a + b)/2

Multiply by 2: 20b + 2a + 2 = 10a + b

19b + 2 = 8a

8a = 19b + 2

Integer Solutions (a, b digits 0–9, a ≠ 0)

Test b = 0 to 9:

• b=0: 8a=2 → a=0.25 ✗
• b=1: 8a=21 → a=2.625 ✗
• b=2: 8a=40 → a=5 ✓
• b=3: 8a=59 → a=7.375 ✗
• b=4: 8a=78 → a=9.75 ✗
• b≥5: 8a>90 → a>9 (invalid digit)

Solution

a=5, b=2 → Alberta's age = 52.

Verification

• Age: 52
• Digits interchanged: 25
• Add 1: 26
• Half of 52 = 26 ✓

Alberta is 52 years old.