Kim is planning a trip to Spain. She will stay there for a total of thirteen nights. She has found two options for her lodging: a hostel, which charges €12.65 (12.65 euros) per night, and a private hotel, which charges €31.25 per night. Kim would like to spend as many nights as she can afford in the private hotel. If she has a budget of €275 for lodging, how many nights can she stay in the hotel?

Let h be the number of hotel nights, so Kim spends 13 − h nights in the hostel. The lodging cost is €31.25h + €12.65(13 − h), which must be at most €275. Six hotel nights would cost €187.50, and the remaining seven hostel nights would cost €88.55, for a total of €276.05—over budget. Five hotel nights cost €257.45 altogether, so she can afford five nights in the private hotel.

AI-written and checked against the verified answer.