1. **State the problem:** Emily has a budget of 720 and wants to rent from either Company A or Company B. Company A charges a setup fee of 80 plus 135 per day. Company B charges 135 per day with no setup fee. We need to find which company allows the maximum number of rental days within the budget. 2. **Formulas:** - Total cost for Company A: $$\text{Cost}_A = 80 + 135d$$ where $d$ is the number of days. - Total cost for Company B: $$\text{Cost}_B = 135d$$ 3. **Calculate maximum days for Company A:** $$80 + 135d \leq 720$$ Subtract 80 from both sides: $$135d \leq 720 - 80$$ $$135d \leq 640$$ Divide both sides by 135: $$d \leq \frac{640}{135} \approx 4.74$$ Since days must be whole numbers, maximum days for Company A is 4. 4. **Calculate maximum days for Company B:** $$135d \leq 720$$ Divide both sides by 135: $$d \leq \frac{720}{135} \approx 5.33$$ Maximum whole days for Company B is 5. 5. **Compare results:** - Company A allows 4 days. - Company B allows 5 days. 6. **Conclusion:** Company B allows for the maximum number of rental days within Emily's budget. **Final answer:** Company B