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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?

Respuesta :

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

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

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