Rudy, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering 608 points for signing up, plus 19 points for every night Rudy books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 25 points, plus 20 points per night. If Rudy 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?

Your vet has placed your pet on a diet. the diet is to contain at least 12 mg of fat and at least 14 mg of protein per serving. these requirements are to be obtained from two food sources. source a contains 2 mg of fat and 2 mg of protein per serving. source b contains 1 mg of fat and 3 mg of protein per serving. if source a sells for $1.28 per serving and source b sells for $1.12 per serving, how many servings of each type should be purchased to satisfy the requirements at minimal cost?