A window repair specialist charges $ 220 for the first two hours of repair plus an hourly fee for each

Question

A window repair specialist charges $ 220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $ 400 . Which function f gives the total cost, in dollars, for x hours of repair, where x &#8805; 2 ?

Accepted Answer

Choice A is correct. It&rsquo;s given that the window repair specialist charges $ 220 for the first two hours of repair plus an hourly fee for each additional hour. Let n represent the hourly fee for each additional hour after the first two hours. Since it&rsquo;s given that x is the number of hours of repair, it follows that the charge generated by the hourly fee after the first two hours can be represented by the expression n x - 2 . Therefore, the total cost, in dollars, for x hours of repair is f x = 220 + n x - 2 . It&rsquo;s given that the total cost for 5 hours of repair is $ 400 . Substituting 5 for x and 400 for f x into the equation f x = 220 + n x - 2 yields 400 = 220 + n 5 - 2 , or 400 = 220 + 3 n . Subtracting 220 from both sides of this equation yields 180 = 3 n . Dividing both sides of this equation by 3 yields n = 60 . Substituting 60 for n in the equation f x = 220 + n x - 2 yields f x = 220 + 60 x - 2 , which is equivalent to f x = 220 + 60 x - 120 , or f x = 60 x + 100 . Therefore, the total cost, in dollars, for x hours of repair is f x = 60 x + 100 . Choice B is incorrect. This function represents the total cost, in dollars, for x hours of repair where the specialist charges $ 340 , rather than $ 220 , for the first two hours of repair. Choice C is incorrect. This function represents the total cost, in dollars, for x hours of repair where the specialist charges $ 160 , rather than $ 220 , for the first two hours of repair, and an hourly fee of $ 80 , rather than $ 60 , after the first two hours. Choice D is incorrect. This function represents the total cost, in dollars, for x hours of repair where the specialist charges $ 380 , rather than $ 220 , for the first two hours of repair, and an hourly fee of $ 80 , rather than $ 60 , after the first two hours.

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