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

Answer:

The shipments are

800 sedans to os Angeles,

400 sedans to Chicago,

500 sedans to Miami.