# SAT Math Multiple Choice Question 818: Answer and Explanation

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**Question: 818**

**8.** A math teacher decides to create several practice tests for her students before theytake the SAT. She wants to make some non-calculator tests and some calculator testsso that her students will be able to practice both. She figures that each non-calculatortest will take her 3 hours to create, and each calculator test will take 4 hours tocreate. If she is willing to devote at most 6 hours per week of her time for the next5 weeks to create the practice tests, and she wants to provide at least 8 practicetests, which of the following systems of inequalities can help her determine how manyof each type of test she can create?

- A.
- B.
- C.
- D.

**Correct Answer:** B

**Explanation:**

**B**

**Difficulty:** Medium

**Category:** Heart of Algebra / Inequalities

**Strategic Advice:** Use the Kaplan Strategy for Translating English into Math. The clue "at least" means that many or more, so use the symbol ≥ when describing the number of tests. The clue "at most" means that many or less, so use the symbol ≤ when describing the number of hours.

**Getting to the Answer:** First assign variables: Let *n* represent the number of non-calculator tests and *c* represent the number of calculator tests. Write an inequality to describe the number of tests:

non-calculator plus calculator is at least 8: *n* + *c* ≥ 8

You can already eliminate C and D. Next, write an inequality to describe the number of hours needed to make the tests. Be sure to incorporate all 5 weeks of time the teacher is willing to devote:

hours per non-calc. test times # of tests: 3*n* plus hours per calc. test times # of tests: + 4*c* is at most 5 hours per week times 6 weeks: ≤ 30

Put the two inequalities together to form the system given in (B).