1. **State the problem:** We are given that the sum of two numbers is 32, and one number is 3 times as large as the other. We need to find both numbers. 2. **Define variables:** Let the smaller number be $x$. Then the larger number is $3x$. 3. **Write the equation:** The sum of the two numbers is 32, so: $$x + 3x = 32$$ 4. **Simplify the equation:** $$4x = 32$$ 5. **Solve for $x$:** $$x = \frac{32}{4} = 8$$ 6. **Find the larger number:** $$3x = 3 \times 8 = 24$$ 7. **Answer:** The smaller number is 8 and the larger number is 24.