1. **State the problem:** We need to find two numbers where the difference between them is 72, and the largest number is 3 less than six times the smaller number. 2. **Define variables:** Let the smaller number be $x$ and the larger number be $y$. 3. **Write the equations based on the problem:** - The difference between the two numbers is 72: $$y - x = 72$$ - The largest number is 3 less than six times the smaller number: $$y = 6x - 3$$ 4. **Substitute the second equation into the first:** $$6x - 3 - x = 72$$ 5. **Simplify the equation:** $$5x - 3 = 72$$ 6. **Add 3 to both sides:** $$5x - \cancel{3} + 3 = 72 + 3$$ $$5x = 75$$ 7. **Divide both sides by 5:** $$\frac{5x}{\cancel{5}} = \frac{75}{\cancel{5}}$$ $$x = 15$$ 8. **Find the larger number $y$ using $y = 6x - 3$:** $$y = 6(15) - 3 = 90 - 3 = 87$$ 9. **Final answer:** The smaller number is $15$ and the larger number is $87$.