1. **State the problem:** Lucario walked 15 miles more than Becks. Together, they walked 27 miles. We need to find how many miles each person walked. 2. **Define variables:** Let $x$ be the miles Becks walked. 3. **Express Lucario's distance:** Lucario walked $x + 15$ miles. 4. **Write the equation for total distance:** $$x + (x + 15) = 27$$ 5. **Simplify the equation:** $$2x + 15 = 27$$ 6. **Isolate $x$ by subtracting 15 from both sides:** $$2x + \cancel{15} - \cancel{15} = 27 - 15$$ $$2x = 12$$ 7. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{\cancel{2}} = \frac{12}{\cancel{2}}$$ $$x = 6$$ 8. **Find Lucario's distance:** $$x + 15 = 6 + 15 = 21$$ 9. **Answer:** Becks walked 6 miles and Lucario walked 21 miles.