1. **State the problem:** We need to find two numbers where their sum is 47, and the smaller number is 23 less than the larger number. 2. **Define variables:** Let the larger number be $x$ and the smaller number be $y$. 3. **Write equations based on the problem:** - The sum of the numbers: $$x + y = 47$$ - The smaller number is 23 less than the larger number: $$y = x - 23$$ 4. **Substitute the second equation into the first:** $$x + (x - 23) = 47$$ 5. **Simplify and solve for $x$:** $$2x - 23 = 47$$ $$2x = 47 + 23$$ $$2x = 70$$ $$x = \frac{70}{2} = 35$$ 6. **Find $y$ using $y = x - 23$:** $$y = 35 - 23 = 12$$ 7. **Answer:** - Larger number: $35$ - Smaller number: $12$