SAT Math Multiple Choice Question 258: Answer and Explanation

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Question: 258

3. A publishing company ships books to schools, some of which are hardback textbooks and some of which are paperback workbooks. Each shipping box can hold a maximum of 20 textbooks or 64 workbooks. Each textbook takes up 192 cubic inches of space, and each workbook takes up 60 cubic inches of space. One box can hold a maximum of 3,840 cubic inches. The shipping department is packing a box containing both types of books. Which of the following systems of inequalities can the department use to determine how many textbooks, t, and workbooks, w, can be shipped in one box?

  • A.
  • B.
  • C.
  • D.

Correct Answer: C

Explanation:

C

Difficulty: Easy

Category: Heart of Algebra / Inequalities

Strategic Advice: Use the Kaplan Method for Translating English into Math. The clue "holds a maximum" means it can hold exactly that much or less, so use the symbol ≤. This means you can eliminate B.

Getting to the Answer: The box can hold a maximum of 20 textbooks, so the first inequality is t ≤ 20. The box can hold a maximum of 64 workbooks, so the second inequality is w ≤ 64 (eliminate D). The third inequality deals with the size of each book. The box can fit t textbooks multiplied by the size of the textbook, 192 cubic inches, and w workbooks multiplied by the size of the workbook, 60 cubic inches. The box can fit a maximum of 3,840 cubic inches total, so the last inequality is 192t + 60w ≤ 3,840.

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