A car rental agency in a major city has a total of 3300 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return patterns are shown in the table (note that Airport means Metropolis Airport).   Rented from Returned to AP DT CA Airport (AP) 90% 10% 10% Downtown (DT) 5% 80% 5% 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 (and hence at the start of the next week)? AP           cars DT           cars CA           cars

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A car rental agency in a major city has a total of 3300 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport. Some weekly rental and return patterns are shown in the table (note that Airport means Metropolis Airport).

  Rented from
Returned to AP DT CA
Airport (AP) 90% 10% 10%
Downtown (DT) 5% 80% 5%


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 (and hence at the start of the next week)?

AP           cars
DT           cars
CA           cars
Expert Solution
Step 1

Given that the A car rental agency in a major city has a total of 3300 cars that it rents from three locations: Metropolis Airport, downtown, and the smaller City Airport.

Let x denote number of cars rented from Metropolis Airport,y denotes number of cars rented from downtown and y denotes number of cars rented from smaller City Airport.

Since car rental agency  has 3300 cars,

x+y+z=3300

From the given table use the information about number of cars returned to Airport form the second equation as,

x=0.9x+0.1y+0.1z0.1x-0.1y-0.1z=0

From the given table use the information about number of cars returned to Downtown form the second equation as,

y=0.05x+0.8y+0.05z0.05x-0.2y+0.05z=0

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