How do g(x), h(x), and f(x) correlate with each other?

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.