SAT Math Multiple Choice Question 117: Answer and Explanation

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Question: 117

12. Samantha offers two different packages of yoga classes at her yoga studio. She offers two hot yoga sessions and three zero gravity yoga sessions at a total cost of $400. She also offers four hot yoga sessions and two zero gravity sessions at a price of $440. Samantha wants to offer a larger package for long-time clients in which the cost must exceed $800. If Samantha does not wish to include more than 13 sessions for the long-time client package, will she be able to create this package for her clients?

  • A. No, because the closest package that she can offer consists of three hot yoga and three zero gravity yoga sessions.
  • B. No, because the closest package that she can offer consists of four hot yoga and four zero gravity yoga sessions.
  • C. Yes, because she can offer five hot yoga and five zero gravity yoga sessions.
  • D. Yes, because she can offer six hot yoga and six zero gravity yoga sessions.

Correct Answer: D

Explanation:

D Translate from English to math in bite-sized pieces. Make the price of a hot yoga lesson h and the price of a zero gravity yoga session z. If she offers 2 hot yoga and 3 zero gravity yoga sessions for $400, then 2h + 3z = 400. Similarly, if 4 hot yoga and 2 zero gravity yoga sessions are $440, then 4h + 2z = 440. Now, be sure to Read the Full Question: You want to know whether Samantha can create a package that's greater than $800 but has fewer than 13 sessions. If you stack the two equations and then add them together, you get 6h + 5z = 880. In other words, she can offer 6 hot yoga and 5 zero gravity yoga sessions (11 total sessions) for $880. This satisfies her requirements, so you know the answer is "Yes"; eliminate (A) and (B). For (C), because you don't know the price of each lesson individually, you don't know yet whether 5 hot yoga and 5 zero gravity yoga sessions will be over $800; leave (C) for now. For (D), if 6 hot yoga and 5 zero gravity yoga sessions were over $800,then adding a zero gravity yoga session will still be over $800. Given what you already know, (D) must be true; choose (D).

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