SAT Math Multiple Choice Question 177: Answer and Explanation

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Question: 177

12. The cost in dollars, C, of producing a custom-made T-shirt with a team logo is given by the formula C = 110 + , where x is the number of T-shirts produced. When every T-shirt produced is sold, the revenue from selling the customized T-shirts is given by R = 15x - . Which one of the following would be the formula for the profit from producing and selling x T-shirts?

(Profit = Revenue - Cost)

  • A. - - x + 110
  • B. - - x + 110
  • C. - + x - 110
  • D. - + x - 110

Correct Answer: C

Explanation:

C Whenever there are variables in the question and in the answers, think Plugging In. If x = 10, then C = 110 + = 110 + 5 = 115 and R = 15 (10) - = 150 - = 150 - 10 = 140. Therefore, the profit can be calculated as 140 - 115 = 25. Plug 10 in for x in the answers to see which answer equals the target number of 25. Choice (A) becomes - - (10) + 110 = - - 31 (5) + 110 = -10 - 155 + 110 = -55. This doesn't match the target number, so eliminate (A). Choice (B) becomes - - (10) + 110 = - - 29(5) + 110 = -10 - 145 + 110 = -45. Eliminate (B). Choice (C) becomes - + (10) - 110 = - + 29(5) - 110 = -10 + 145 - 110 = 25. Keep (C), but check (D) just in case it also works. Choice (D)becomes - + (10) - 110 = - + 31(5) - 110 = -10 + 155 - 110 = 35. Eliminate (D) and choose (C).

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