1. **State the problem:** The present ages of two friends add up to 50. Six years ago, one friend's age was twice the age of the other. 2. **Define variables:** Let the present age of the first friend be $x$ and the second friend be $y$. 3. **Write equations:** - The sum of their present ages is $x + y = 50$. - Six years ago, the first friend's age was $x - 6$ and the second friend's age was $y - 6$. - According to the problem, $x - 6 = 2(y - 6)$. 4. **Solve the system:** From the first equation, express $y$ as $y = 50 - x$. Substitute into the second equation: $$x - 6 = 2((50 - x) - 6)$$ $$x - 6 = 2(44 - x)$$ $$x - 6 = 88 - 2x$$ 5. **Simplify and solve for $x$:** $$x - 6 + 2x = 88$$ $$3x - 6 = 88$$ $$3x = 94$$ $$x = \frac{94}{3}$$ 6. **Calculate $y$:** $$y = 50 - x = 50 - \frac{94}{3} = \frac{150}{3} - \frac{94}{3} = \frac{56}{3}$$ 7. **Final answer:** The present ages are $\frac{94}{3} \approx 31.33$ years and $\frac{56}{3} \approx 18.67$ years.