1. **Stating the problem:** We are given that the sum of two numbers is 40 and one number is twice the other. 2. **Forming the equations:** Let the two numbers be $x$ and $y$. From the problem: - The sum of the two numbers is 40: $$x + y = 40$$ - One number is twice the other: $$y = 2x$$ 3. **Substitute the second equation into the first:** $$x + \cancel{y} = 40$$ $$x + \cancel{2x} = 40$$ $$x + 2x = 40$$ 4. **Simplify:** $$3x = 40$$ 5. **Solve for $x$:** $$x = \frac{40}{3}$$ 6. **Find $y$ using $y = 2x$:** $$y = 2 \times \frac{40}{3} = \frac{80}{3}$$ 7. **Final answer:** The two numbers are $$x = \frac{40}{3}$$ and $$y = \frac{80}{3}$$.