SAT Math Multiple Choice Question 312: Answer and Explanation

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Question: 312

12. In Delray Beach, Florida, you can take a luxury golf cart ride around downtown. The driver charges $4 for the first mile, plus $1.50 for each additional mile. Which inequality represents the number of miles, m, that you could ride and pay no more than $10?

  • A. 3.25 + 1.5m ≤ 10
  • B. 3.25 + 3m ≤ 10
  • C. 4 + 1.5m ≤ 10
  • D. 4 + 3m ≤ 10

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Heart of Algebra / Inequalities

Strategic Advice: Pay careful attention to units, particularly when a question involves rates. The $4.00 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 driver charges $4.00 for the first mile, which is a flat fee, so write 4. The additional charge is $1.50 per mile, or 1.50 times 2 = $3.00 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 $10" means that much or less, so use the symbol ≤. The inequality is , which simplifies to 3.25 + 3m ≤ 10.

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