PSAT Math Multiple-Choice Question 18: Answer and Explanation

Question: 18

A ski resort is renting skis for $30 and snowboards for $20 over a weekend. On Friday, 40 skis and snowboards were rented, and the resort collected $1,100 in rental fees. On Saturday, 55 skis and snowboards were rented and the resort collected $1,400 in rental fees. On Sunday, the resort rented 85 skis and snowboards and collected $2,100 rental fees. Solving which of the following system of equations yields the number of skis, s, and the number of snowboards, b, that were rented over the three-day weekend?

• A. s + b = 50
  30s + 20b = 180
• B. s + b = 180
  30s + 20b = 460
• C. s + b = 180
  30s + 20b = 4,600
• D. s + b = 4,600
  30s + 20b = 180

Correct Answer: C

Explanation:

C

The question asks for a system of equations that can be solved to find the number of skis and the number of snowboards rented over the three-day weekend. Use Bite-Sized Pieces and translate the given information into equations. Start with the number of skis and snowboards. The number of skis and snowboards rented on Friday was 40, on Saturday was 55, and on Sunday was 85. The total number of skis and snowboards rented for the weekend is 180. In equation form, s + b = 180. Eliminate (A) and (D), which both contain the incorrect equation for the number of skis and snowboards rented. Next write an equation for the amount of money collected in rental fees. Skis are rented for $30 and snowboards are rented for $20. The rental fees collected were $1,100 on Friday, $1,400 on Saturday, and $2,100 on Sunday. The total amount of fees collected was $4,600. In equation form 30s + 20b = 4,600. Eliminate (B), which contains the incorrect equation for rental fees collected. The correct answer is (C).