PSAT Math Multiple-Choice Question 350: Answer and Explanation

Question: 350

A local airport has separate fees for commercial airliners and private planes. Commercial flights are charged a landing fee of $281 per flight and private planes are charged a landing fee of $31 per flight. On a given day, a total of 312 planes landed at the airport and $47,848 in landing fees was collected. Solving which of the following systems of equations yields the number of commercial airliners, c, and the number of private planes, p, that landed at the airport on the day in question?

• A.
• B.
• C.
• D.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Word Problems

Getting to the Answer: Because the variables are defined in the question stem and because the answer choices contain the variables, the only thing left for you to do is to figure out how they relate to one another. There will be two equations: one involving the total number of aircraft that landed and one involving the total amount of landing fees collected. Add together both types of aircraft to get the total number of aircraft that landed: c + p = 312. Think carefully about which type of plane should be associated with which fee to get the latter. Commercial airliners are much more expensive; hence, your second equation should be 281c + 31p = 47,848. Only (C) contains both of those equations.