PSAT Math Multiple-Choice Question 193: Answer and Explanation

Question: 193

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 $20.00 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 + 2 m ≤ 20
• B. 3 + 0.25 m ≤ 20
• C. 3 + 2 m ≤ 20
• D. 12 + 2 m ≤ 20

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Heart of Algebra/Inequalities

Getting to the Answer: Pay careful attention to units, particularly when a question involves rates. 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 ′ 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 + 2 m ≤ 20, (A).