SAT Math Multiple Choice Question 155: Answer and Explanation

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Question: 155

5. Régine is measuring how many solutions from Batch x and Batch y are acidic. She measured a total of 100 solutions from both batches. 40% of the solutions from Batch x and 70% of the solutions from Batch y were acidic, for a total of 48 acidic solutions. Solving which of the following systems of equations yields the number of solutions in Batch x and Batch y ?

  • A. x + y = 100
    0.4x + 0.7y = 48
  • B. x + y = 48
    0.4x + 0.7y = 100
  • C. x + y = 100 × 2
    0.4x + 0.7y = 48
  • D. x + y = 100
    40x + 70y = 48

Correct Answer: A

Explanation:

A Start with the easier equation first and use Process of Elimination. The easier equation has to do with the total number of solutions. According to the question, Régine measures a total of 100 solutions. This information can be expressed as x + y = 100. Eliminate (B) and (C) because neither of these answers includes this equation. Remember that percentage means divided by 100. Therefore, 40% = 0.4 and 70% = 0.7. Given this information, x should be associated with 0.4 and y should be associated with 0.7. On this basis eliminate (D). The correct answer is (A).

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