SAT Math Multiple Choice Question 742: Answer and Explanation

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Question: 742

7. During a 40-minute session at a 220 volt charging station, the charge on an electric car battery increases from an initial charge of 50 power units to a final charge of 106 power units. If this charge increases linearly with time, which of the following best describes the charge, q, in power units, on this same battery after charging for t hours from an initial charge of 20 power units? (1 hour = 60 minutes)

  • A. q = 55t + 50
  • B. q = 84t + 50
  • C. q = 55t + 20
  • D. q = 84t + 20

Correct Answer: D

Explanation:

D

Advanced Mathematics (quadratics) MEDIUM-HARD

Read the question carefully, and note particularly what it is asking for and what information can help you find it. We are asked to find an equation to relate two variables, q, the number of power units, and t, the number of hours the battery has been charging. We are told that the initial charge is 20 power units, so q = 20 when t = 0. We are also told that the charge increases from 50 power units to 106 power units in 40 minutes. But since our time unit t is in hours, we should convert 40 minutes to 40/60 = 2/3 hours. Therefore, the charging station charges at a rate of (106 - 50)/(2/3) = (56)/(2/3) = 84 charging units per hour. This unit rate is the slope of the line, as we discussed in Chapter 8, Lesson 5. Therefore, the equation should represent a line with slope of 84 that contains the point t = 0 and q = 20, which is the equation in (D) q = 84t + 20.

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