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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 ≥ 2 dollars, for x hours of repair, where x? = 60x+100
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
$220 Choice A is correct. It’s given that the window repair specialist charges 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 2h. Therefore, the total cost, in dollars, for x hours of repair is =220+ -2 $400 f^xh n^x h. It’s given that the total cost for 5 hours of repair is . 400 =220+ -2 Substituting 5 for x and for f^xh into the equation f^xh n^x h 400=220+ 5-2 400=220+3 220 yields n^ h, or n. Subtracting from both sides 180=3 of this equation yields n. Dividing both sides of this equation by 3 yields =60 60 =220+ -2 n . Substituting for n in the equation f^xh n^x h yields =220+60 -2 =220+60 -120 f^xh ^x h, which is equivalent to f^xh x , or =60 +100 f^xh x . Therefore, the total cost, in dollars, for x hours of repair is =60 +100 f^xh x . Choice B is incorrect. This function represents the total cost, in dollars, for $340 $220 x hours of repair where the specialist charges , rather than , for the first two hours of repair. Choice C is incorrect. This function represents the total $160 cost, in dollars, for x hours of repair where the specialist charges , rather $220 $80 than , for the first two hours of repair, and an hourly fee of , rather than $60 , after the first two hours. Choice D is incorrect. This function represents the $380 total cost, in dollars, for x hours of repair where the specialist charges , $220 $80 rather than , for the first two hours of repair, and an hourly fee of , rather $60 than , after the first two hours.
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