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This case study is all about solving a system of equations using the RREF of a matrix. (Section 2.2)
A car rental agency in a major city has a total of 2200 cars that it rents from three locations: Metropolis Airport, downtown and at the smaller City Airport. Some weekly rental and return patterns are shown in the table
Rented From
Returned to
Metropolis Airport
Downtown
City Airport
90%
10%
5%
80%
At the beginning of a week, how many cars should be at each location so that the same number of cars will be there at the end of the week?
Start by writing a system of equations using three variables that represent the amount of rental cars at each airport. Then convert this to an augmented matrix and put it in RREF using your calculator. Finally interpret the results.
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