A software company is selling a new game in a standard edition and a collector’s edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector’s edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector’s edition games, c, that were ordered?

Options

A. 75-s=c
20s+30c=1,870
B. 75-s=c
30s+20c=1,870
C. s-c=75
25(s+c)=1,870
D. s-c=75
30s+20c=1,870

Answer

A

Explanation

The total number of copies of the game the company will ship is 75, so one equation in the system is s + c = 75, which can be written as 75 − s = c. Because each standard edition of the game has a volume of 20 cubic inches and s represents the number of standard edition games, the expression 20s represents the volume of the shipment that comes from standard edition copies of the game. Similarly, the expression 30c represents the volume of the shipment that comes from collector’s edition copies of the games. Because these volumes combined are 1,870 cubic inches, the equation 20s + 30c = 1,870 represents this situation. Therefore, the correct answer is choice A.
Choice B is incorrect. This equation gives the volume of each standard edition game as 30 cubic inches and the volume of each collector's edition game as 20 cubic inches. Choice C is incorrect. This is the result of finding the average volume of the two types of games, using that average volume (25) for both types of games, and assuming that there are 75 more standard editions of the game than there are collector’s editions of the game. Choice D is incorrect. This is the result of assuming that the volume of each standard edition game is 30 cubic inches, that the volume of each collector's edition game is 20 cubic inches, and that there are 75 more standard editions than there are collector’s editions.