Elisa and Katy are both traveling to Europe. Elisa paid $820 for her plane ticket and $110.50 per night for her hotel. Katy paid $1,205 for her plane ticket and $75.50 per night for her hotel. They each spent the same number of nights in their hotels. The two women each spent the same total amount for airfare and lodging during their trips. Set up a system of equations to model the amount of money Elisa and Katy spend on airfare and lodging during their trips. Let x represent the number of nights spent in a hotel, let E represent the total amount Elisa spends, and let K represent the total amount Katy spends.​