Awildlife service wanted to estimate the number of alligators in a river so they tagged 90 alligators and released them back into the river. later they found that a sample of 200 alligators contained 23 that were tagged. assuming that the tagged alligators are evenly distributed, what is the best estimate of the number of alligators in the river?

this is from a practice test i found online for a placement test for a community college. i have never encountered these type of word problems before. i don't even know where to start.

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.)