1. **State the problem:** Maria has a budget of 90 to rent a car from Katey's Kars, which charges 78 per day plus 0.43 per kilometer. We need to find the maximum distance Maria and her grandmother can travel, including the return trip, within the 90 budget. 2. **Define variables and write the cost equation:** Let $d$ be the total distance traveled (including the return trip) in kilometers. The total cost $C$ is given by the sum of the daily rental and the cost per kilometer: $$C = 78 + 0.43d$$ 3. **Set up the inequality for the budget:** Since Maria's budget is 90, the total cost must be less than or equal to 90: $$78 + 0.43d \leq 90$$ 4. **Solve for $d$:** Subtract 78 from both sides: $$\cancel{78} + 0.43d \leq 90 - \cancel{78}$$ $$0.43d \leq 12$$ Divide both sides by 0.43: $$\frac{0.43d}{0.43} \leq \frac{12}{0.43}$$ $$d \leq \frac{12}{0.43}$$ Calculate the division: $$d \leq 27.9069767...$$ 5. **Interpret the result:** Maria and her grandmother can travel up to approximately 27.91 kilometers total, including the return trip, without exceeding the 90 budget. **Final answer:** $$\boxed{27.91 \text{ kilometers}}$$