OG详解-OG10 数学1 Q26

Choice A is correct. It’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’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’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+3n. Subtracting 220 from both sides of this equation yields 180 = 3n. Dividing both sides of this equation by 3 yields n = 60. Substituting 60 for n in the equation f(x) = 220+n(x-2) yieldsf(x) = 220+60(x-2), which is equivalent to f(x) = 220+60x-120, or f(x) = 60x+100. Therefore, the total cost, in dollars, for x hours of repair is f(x) = 60x+ 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.