A repair company offers two levels of service, Standard and Premium. The total cost for a repair consists of a fixed se…

Let C be the total cost, h be the number of hours, r be the hourly rate, and F be the fixed service fee. The relationship is a linear function: C = rh + F.

First, determine the hourly rate and fixed fee for the Standard service. We have two data points: (2, 130) and (5, 280). We can set up a system of two linear equations, where r_s is the Standard hourly rate:

1) 130 = 2r_s + F

2) 280 = 5r_s + F

Subtracting the first equation from the second gives: (280 - 130) = (5r_s - 2r_s) + (F - F), which simplifies to 150 = 3r_s. Solving for r_s gives r_s = 50. The hourly rate for Standard service is $50.

Substitute r_s = 50 into the first equation: 130 = 2(50) + F, so 130 = 100 + F. Solving for F gives F = 30. The fixed service fee is $30.

The problem states the fixed fee is the same for Premium service, so for Premium service, F = 30. We are given that a 3-hour Premium repair costs $240. We can find the Premium hourly rate, r_p:

240 = 3r_p + 30

210 = 3r_p

r_p = 70. The hourly rate for Premium service is $70.

The question asks for the total cost of a 4-hour Premium service repair. Using the Premium rate (r_p = 70) and the fixed fee (F = 30):

C = 70(4) + 30

C = 280 + 30

C = 310

The total cost is $310.

Choice A is incorrect; $230 is the cost of a 4-hour Standard service repair (50(4) + 30), not Premium.

Choice B is incorrect; $280 is the variable cost component for a 4-hour Premium repair (70(4)), but it omits the fixed $30 service fee.

Choice D is incorrect; $320 results from incorrectly calculating the Premium hourly rate by ignoring the fixed fee (r_p = 240/3 = 80), and then calculating the cost for 4 hours based on this incorrect rate (80 · 4 = 320).