SAT Math Multiple Choice Question 358: Answer and Explanation

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Question: 358

13. A taxi in the city charges $3.00 for the first mile, plus $0.25 for each additional mile. Eric plans to spend no more than $20 on a taxi ride around the city. Which inequality represents the number of miles, m, that Eric could travel without exceeding his limit?

  • A. 2.5 + 2m ≤ 20
  • B. 3 + 0.25m ≤ 20
  • C. 3 + 2m ≤ 20
  • D. 12 + 2m ≤ 20

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Heart of Algebra / Inequalities

Strategic Advice: Pay careful attention to units, particularly when a question involves rates. The $3.00 for the first mile is a flat fee. Before you write the inequality, you need to find the per mile rate for the remaining miles.

Getting to the Answer: The taxi charges $3.00 for the first mile, which is a flat fee, so write 3. The additional charge is $0.25 per mile, or 0.25 times 8 = $2.00 per mile. The number of miles after the first mile is , so the cost of the trip, not including the first mile is . This means the cost of the whole trip is . The clue "no more than $20" means that much or less, so use the symbol ≤. The inequality is , which simplifies to 2.5 + 2m ≤ 20.

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