1. The problem: Solve the ratio problem where the ratio of two numbers is 3:5 and their sum is 64. Find the two numbers. 2. Formula and rules: If two numbers are in the ratio $a:b$, then the numbers can be expressed as $3x$ and $5x$ for some $x$. 3. Set up the equation using the sum: $$3x + 5x = 64$$ 4. Simplify the equation: $$8x = 64$$ 5. Solve for $x$: $$x = \frac{64}{8}$$ 6. Simplify the fraction with cancellation: $$x = \frac{\cancel{64}}{\cancel{8}} = 8$$ 7. Find the two numbers: $$3x = 3 \times 8 = 24$$ and $$5x = 5 \times 8 = 40$$ 8. Final answer: The two numbers are 24 and 40. This problem demonstrates how to use ratios to find actual values when given a total sum.