1. **State the problem:** We are given two numbers where one number is twice the other, and their sum is 51. We need to find these two numbers. 2. **Set variables:** Let the smaller number be $x$. Then the larger number is $2x$ because it is twice the smaller number. 3. **Write the equation:** The sum of the two numbers is 51, so: $$x + 2x = 51$$ 4. **Simplify the equation:** $$3x = 51$$ 5. **Solve for $x$:** $$x = \frac{51}{3}$$ $$x = 17$$ 6. **Find the other number:** The larger number is twice $x$, so: $$2x = 2 \times 17 = 34$$ 7. **Answer:** The two numbers are 17 and 34.