A man was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago and you will know how old I am." What is the age of the man?

### Concept & Logic This is a direct word-to-algebra translation problem. Simply map the man's convoluted statement into a single linear equation representing his present age. $$ x = 3(x + 3) - 3(x - 3) $$ ### Step-by-Step Solution * **Given:** Present age = 3 $\times$ (Age in 3 years) - 3 $\times$ (Age 3 years ago). * **Calculation:** Let the man's present age be $x$. * Age 3 years hence = $x + 3$. * Age 3 years ago = $x - 3$. * Construct the equation based on his statement: $x = 3(x + 3) - 3(x - 3)$. * Expand both terms: $x = (3x + 9) - (3x - 9)$. * Distribute the negative sign carefully: $x = 3x + 9 - 3x + 9$. * Combine like terms: The $3x$ and $-3x$ cancel each other out. * $x = 18$. ### Exam Strategy & Shortcut **Pattern Recognition:** Notice the structure $a(x + y) - a(x - y)$. This expands to $ax + ay - ax + ay$, which always simplifies to $2ay$. In this problem, $a=3$ and $y=3$. So the result is simply $2(3)(3) = 18$. The $x$ terms completely disappear, making it an instant calculation. ### Common Pitfall Failing to distribute the negative sign properly on the second term. Writing $(3x + 9) - 3x - 9 = 0$ leads to a nonsensical result and panic during the exam. ### Final Answer Therefore, the correct answer is **18 years**.