1. **State the problem:** We need to find the cost of each ride given the total cost and the number of times each ride was taken by Mike and Gavin. 2. **Define variables:** Let $x$ be the cost of one ride on the Roller Coaster. Let $y$ be the cost of one ride on the Gravity Free-Fall. 3. **Write equations from the tickets:** From Mike's ticket (3 Roller Coaster rides and 3 Gravity Free-Fall rides): $$3x + 3y = 36$$ From Gavin's ticket (2 Roller Coaster rides and 3 Gravity Free-Fall rides): $$2x + 3y = 29.5$$ 4. **Solve the system of equations:** Subtract the second equation from the first: $$\cancel{3x} + 3y = 36$$ $$- (\cancel{2x} + 3y = 29.5)$$ Gives: $$x = 36 - 29.5 = 6.5$$ 5. **Find $y$ by substituting $x=6.5$ into one equation:** Using $2x + 3y = 29.5$: $$2(6.5) + 3y = 29.5$$ $$13 + 3y = 29.5$$ $$3y = 29.5 - 13 = 16.5$$ $$y = \frac{16.5}{3} = 5.5$$ 6. **Final answer:** - Cost of Roller Coaster ride $x = 6.5$ - Cost of Gravity Free-Fall ride $y = 5.5$