SAT Math Multiple Choice Question 362: Answer and Explanation

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Question: 362

2. As a general rule, businesses strive to maximize revenue and minimize expenses. An office supply company decides to try to cut expenses by utilizing the most cost-effective shipping method. The company determines that the cheapest option is to ship boxes of ballpoint pens and mechanical pencils with a total weight of no more than 20 pounds. If each pencil weighs 0.2 ounces and each pen weighs 0.3 ounces, which inequality represents the possible number of ballpoint pens, b, and mechanical pencils, m, the company could ship in a box and be as cost-effective as possible?

  • A. 0.3b + 0.2m < 20
  • B. 0.3b + 0.2m ≤ 20
  • C.
  • D.

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Heart of Algebra / Inequalities

Strategic Advice: Think about this question conceptually. The box cannot weigh more than 20 pounds, so start there. If the box cannot weigh more than 20 pounds, this means it can weigh 20 pounds or less, so the right half of the inequality you are looking for is ≤20. This means you can eliminate A and C.

Getting to the Answer: Again, think about the question. A box is made up of ballpoint pens, b, and mechanical pencils, m. Each pen weighs 0.3 ounces, and each pencil weighs 0.2 ounces. The total weight of the box would be the number of pens, b, multiplied by their weight, 0.3, added to the number of pencils, m, multiplied by their weight, 0.2. So the inequality is 0.3b + 0.2m ≤ 20.

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