SAT Math Multiple Choice Question 804: Answer and Explanation

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Test Information

Question: 804

9. In addition to the standard airfare, a particular airline charges passengers for twokinds of travel services: $25 to check a bag and $15 to upgrade to priority boarding.If the airline collected $3,065 in baggage and priority boarding fees from 145 travelservices on two flights combined, which of the following systems of equations couldbe used to determine the number of bags checked (b) and the number of priority boarding upgrades (p) purchased on the two flights?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Strategic Advice: When matching a real-world scenario to a system of equations, always look carefully at the operations in each equation as well as the coefficients on the variables.

Getting to the Answer: You're given two variables: b for bags checked and p for priority boarding upgrades. The question states that 145 travel services were charged for two flights combined (not on each flight), so the first equation should be b + p = 145. Eliminate A and D. Similarly, the airline collected $3,065 in fees on these two flights. Because a checked bag costs $25 and priority boarding costs $15, the second equation is 25b + 15p = 3,065. Choice (B) is the only answer that contains both correct equations.

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