Ages (algebraic identity puzzle): “Take my age three years hence, multiply it by 3, then subtract 3 times my age three years ago; you will get my present age.” Find my age.

Introduction / Context:This is a neat identity-based age puzzle. The arithmetic structure collapses to a constant regardless of the unknown age, allowing a one-line solution when the algebra is set up correctly.

Given Data / Assumptions:Let present age be x. The statement translates to 3(x + 3) − 3(x − 3) = x.

Concept / Approach:Compute the left-hand expression and equate to x. Simplification reveals a fixed value for x.

Step-by-Step Solution:

Verification / Alternative check:Plug back: in 3 years, 21; 3*21 = 63. Three years ago, 15; 3*15 = 45. Difference 63 − 45 = 18, which equals the present age (✓).

Why Other Options Are Wrong:They do not satisfy the identity when substituted.

Common Pitfalls:Expanding incorrectly or forgetting that subtracting 3(x − 3) changes signs for both terms.

Final Answer:18