SAT Math Multiple Choice Question 179: Answer and Explanation

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Question: 179

14. Peter's Petrol Station is selling regular unleaded gas for $3.49 a gallon and premium gas for $3.79 a gallon. If a car wash is purchased, then a discount of $0.10 per gallon is applied. During one morning, a total of 850 gallons of gas was sold, and 100 gallons were sold at the discounted rate. The total collected in sales was $3,016.50. Solving which of the following systems of equations yields the number of regular unleaded gallons of gas, u, and the number of premium gallons of gas, p, that were sold during that morning?

  • A. u + p = 850
    3.49u + 3.79p = 301.65
  • B. u + p = 850
    3.49u + 3.79p = 3,016.50
  • C. u + p = 850
    3.49u + 3.79p = 3,026.50
  • D. u + p = 3,016.50
    3.49u + 3.79p = 850

Correct Answer: C

Explanation:

C Start with the easier equation first and use Process of Elimination. The easier equation involves the total amount of gas sold.According to the question, 850 gallons of gasoline were sold, which can be expressed as u + p = 850. Eliminate (D) since it does not include this equation. The other equation in the answers is related to the amount of money collected. According to the question, $3,016.50 was collected; however, this sum included a discount of $0.10 per gallon for 100 of the gallons that were purchased or $0.10 × 100 = $10. Without the discount unleaded gas costs $3.49 and premium gas costs $3.79 a gallon, and the amount of money collected would have been $3,016.50 + $10 = $3,026.50. Only (C) provides the correct total. Therefore, the correct answer is (C).

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