1. **State the problem:** Kimberly wants to find the number of bus rides where the total cost of paying per ride equals the total cost of buying a bus pass plus a reduced per-ride cost. 2. **Define variables:** Let $x$ be the number of bus rides. 3. **Write the cost expressions:** - Cost without pass: $2.50x$ - Cost with pass: $15 + 1.00x$ 4. **Set up the equation for equivalence:** $$2.50x = 15 + 1.00x$$ 5. **Solve the equation:** Subtract $1.00x$ from both sides: $$2.50x - 1.00x = 15$$ $$1.50x = 15$$ Divide both sides by $1.50$: $$x = \frac{15}{1.50} = 10$$ 6. **Interpretation:** After 10 rides, the cost of both options is the same. For more than 10 rides, the bus pass option is cheaper. **Final answer:** Kimberly needs to take 10 rides for the costs to be equivalent.