SAT Math Multiple Choice Question 143: Answer and Explanation

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Question: 143

8. Each winter, Captain Dan's Ski Lodge rents both pairs of skis and snowboards to its guests for a flat daily rate per pair of skis and a flat daily rate per snowboard. Five pairs of skis and two snowboards will cost a family $370. Three pairs of skis and four snowboards will cost a family $390. During a particularly slow season, Captain Dan announces a 10% discount on all skis and snowboards. What would be the cost of renting two pairs of skis and two snowboards if they were rented during this discount period?

  • A. $99
  • B. $110
  • C. $198
  • D. $220

Correct Answer: C


CIn order to determine the normal cost for renting skis and snowboards, you need to write two equations and then manipulate and solve those equations. If you call skis x and snowboards y, your two equations will be 5x + 2y = 370 and 3x + 4y = 390. Look for a way to stack and add the equations to eliminate one of the variables. For instance, multiply the first equation by 2 to get 10x + 4y = 740, and then stack and subtract the equations, as follows:

So, 7x = 350 and x = 50, so the price of a pair of skis is $50. Plug this number back into either equation to find the cost of a snowboard: 10(50) + 4y = 740, so 4y = 740 - 500 and 4y = 240. Therefore, y = 60, the cost of a snowboard. So, the cost of two pairs of skis and two snowboards would normally be 2(50) + 2(60) = 100 + 120 = 220. Finally, remember that prices are discounted by 10%, so multiply the price of $220 by 10% to get $22, and subtract $22 from the price. The final cost of two pairs of skis and two snowboards is 220 - 22 = 198, which is (C).

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