My age in six years

Statement

Seven years ago I was one third of the age I will be in three years. How old will I be in six years?

Solution

Unknown. Let $x$ be my age today.

Equation. Seven years ago I was $x-7$; in three years I will be $x+3$. The condition gives: $x-7 = \frac{1}{3}(x+3).$ Multiply by $3$: $3x-21 = x+3 \implies 2x = 24 \implies x = 12.$ So I am $12$ today; in six years I will be $12+6=18$. Check: seven years ago I was $5$; in three years I will be $15$; and $5 = \tfrac13\cdot 15$. Correct. $\boxed{18 \text{ years}}$