SAT Math Multiple Choice Question 795: Answer and Explanation

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Question: 795

15. Two garages each charge a fixed amount, plus an hourly rate, to service a car. Thegarage on Main Street charged one customer $153 for a 2-hour service appointment,and it charged a second customer $315 for a 5-hour service appointment. The garageon 2nd Street charges $5 less per hour than the garage on Main Street and $10 morefor the fixed amount. How much would the garage on 2nd Street charge for a 3-hourservice appointment?

  • A. $157
  • B. $174
  • C. $181
  • D. $202

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Heart of Algebra / Linear Equations

Strategic Advice: In a question like this, take a few seconds to plan a route to the desired quantity. For example, before you can determine the amount that the garage on 2nd Street would charge, you'll need to find the hourly rate and the fixed amount charged by the garage on Main Street. To do this, think about what aspect of a linear relationship could tell you the hourly rate.

Getting to the Answer: In a real-world scenario, a unit rate (here, the hourly rate) is the same as slope. To find the slope, start by writing the amounts given as ordered pairs in the form (hours, amount); the ordered pairs are (2, 153) and (5, 315). Now, plug these values into the slope formula:. The garage on Main Street charges $54 per hour. The garage on 2nd Street charges $5 less per hour, or $54 - $5 = $49 per hour. Now you need to find the fixed amount charged by the garage on Main Street. If a customer was charged $153 for 2 hours, and the hourly rate is $54 per hour, then the fixed amount is $153 - 2($54) = $45. The garage on 2nd Street charges $10 more for the fixed amount, or $45 + $10 = $55. Put the two pieces of information together to find that the garage on 2nd Street would charge $55 + 3($49) = $202 for a 3-hour service appointment, which is (D).

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