Chad, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering 472 points for signing up, plus 95 points for every night Chad books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 516 points, plus 73 points per night. If Chad books a certain number of nights, the points he earns with either hotel will be the same. How many nights will that be? How many points will he have?