SAT Math Multiple Choice Question 69: Answer and Explanation

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Question: 69

9. A dental hygiene company is creating a new 24-ounce tube of toothpaste by combining its most popular toothpastes, Cavity Crusher and Bad Breath Obliterator. Cavity Crusher contains 0.25% of sodium fluoride as its active ingredient, and Bad Breath Obliterator contains 0.30% of triclosan as its active ingredient for a total of 0.069 ounces of active ingredients in both toothpastes. Solving which of the following systems of equations yields the number of ounces of Cavity Crusher, c, and the number of ounces of Bad Breath Obliterator, b, that are in the new toothpaste?

  • A. c + b = 0.069
    0.25c + 0.3b = 24
  • B. c + b = 24
    0.0025c + 0.003b = 0.069
  • C. c + b = 24
    0.025c + 0.03b = 0.069
  • D. c + b = 24
    0.25c + 0.3b = 0.069

Correct Answer: B


B Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of ounces, c + b, in the tube. According to the question, the tube has 24 ounces, so c + b = 24. Eliminate (A), since it does not include this equation. The other equation in the set is related to the amount of active ingredients. According to the question, c includes 0.25% of sodium fluoride and b contains 0.30% triclosan. 0.25% = 0.0025 and 0.30% = 0.003. Therefore, in the correct equation, c should be associated with 0.0025 and b should be associated with 0.003. Eliminate (C) and (D) because both of these equations get the percentages wrong. The correct answer is (B).

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