A group of 10 students went to a football game at their university. They each bought a ticket for $x and spent $20 on a t-shirt. A group of 4 adults went to the same football game and paid five times as much for each of their tickets as each student. The group of adults also bought a long-sleeved t-shirt for $25 each. The group of students spent the same amount as the group of adults. What is the cost of each student ticket? Write and solve an equation to model the problem.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)