Reliable auto company wants to ship 1700 1700 status sedans to three major dealers in los angeles, chicago, and miami. from past experience reliable figures that it will sell twice as many sedans in los angeles as chicago. it costs $ 230 230 to ship a sedan to los angeles, $ 70 70 to chicago, and $ 160 160 to miami. if reliable auto has paid $ 292 , 000 292 000 to pay for shipping costs, how many sedans should it ship to each city?

Define
x = number of sedans shipped to Los Angeles
y = number of sedans shipped to Chicago
z = number of sedans shipped to Miami

Because the total number of sedans shipped is 1700, therefore
x + y + z = 1700          (1)

The company expects to ship twice as many sedans to Los Angles as to  Chicago. Therefore
x = 2y                        (2)

The total shipping cost is $292,000. The shipping costs per sedan are
$230 to Los Angeles, $70 to Chicago, and $160 to Miami.
Therefore
230x + 70y + 160z = 292,000
or
23x + 7y + 16z = 29200       (3)

Substitute (2) into (1).
2y + y + z = 1700              
3y + z = 1700
z = 1700 - 3y                    (4)

Substitute (2) into (3).
23(2y) + 7y + 16z = 29200
53y + 16z = 29200            (5)

Substitute (4) into (5).
53y + 16(1700 - 3y) = 29200
5y + 27200 = 29200
5y = 2000
y = 400

From (2), obtain
x = 2*400 = 800
From (4), obtain
z = 1700 - 3*400 = 500

 
The shipments are
800 sedans to os Angeles,
400 sedans to Chicago,
500 sedans to Miami.

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