Airam Salinas & Fatima Gonzalez December 18, A

A cruise ship has 680 rooms. Those with a view rent for $160 per night and those without a view rent for $105 per night. On a night when the ship was completely occupied, revenues were $92,500. How many of each type of room are on the ship? PROBLEM SITUATION

The variables in these equation are A which represents the number of rooms with a view, which costs $160 per night, and F which represents the number of rooms without a view, which costs $105 per night. DEFINE VARIABLES

Our system of equations are ∆ 92,500 = 160A + 105F ∆ A + F = 680 SYSTEM OF EQUATIONS

First you need to rewrite one of the equations: A + F = 680 Solve for F: F = A Now substitute into the other equation = 160A + 105(680-A) = 160A A = 55A = 55A 21100/55 = A To solve this equation you will have to use substitution. SOLUTION METHOD A= F=296.36

(A, F) (383.64, ) SOLUTION TO THE SYSTEM OF EQUATIONS

∆92,500 = 160(383.64) + 105(296.36) True ∆ = 680 True CHECK OF SOLUTION

The number of rooms has to be a whole number in order to make sense in this problem situation is the number of rooms with a view is the number of rooms without a view. SOLUTION IN THE PROBLEM SITUATION