SAT Math Multiple Choice Question 287: Answer and Explanation

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Question: 287

2. A hospital hosts an annual charity drive in which volunteers sell first aid kits to raise money for the pediatric ward. The hospital ordered too many kits last year, so it already has some to start this year's drive with. The project manager estimates, based on last year's sales, that the hospital needs to order an additional 50 boxes of kits. The function k(b) = 12b + 32, where b is the number of boxes ordered, represents the number of kits the hospital will have after the order arrives. When the project manager places the order, she is told that the company has changed the number of kits per box to 8. How many more boxes will she need to order to end up with the same number of kits that she had originally planned for?

  • A. 25
  • B. 32
  • C. 75
  • D. 200

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: Start by determining what each part of the function given represents.

Getting to the Answer: The function represents the number of kits the hospital will have, so k(b) is the total number of kits. The question tells you that b is the number of boxes ordered, which you also know to be 50. Because b is multiplied by 12, this must be the number of kits per box. Finally, 32 is simply added to the equation, which must mean it represents the kits left over from last year's charity drive. Now, look at the question. It states that the company has changed the number of kits per box to 8. Evaluate the original function at b = 50 to see how many kits the hospital would have had: k(50) = 12(50) + 32 = 632.

Now, substitute this for k(b) in the new function, replacing the 12 with the 8, and solve for b:

Be careful-this is not the answer. She needs to order 75 - 50 = 25 more boxes than she would have had to order at 12 kits per box.

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