Video: US-SAT03S4-Q22-385139324021

A video game company released a new game with two versions: a standard version and a deluxe one. The standard version costs $55.50 and the deluxe one costs $64.50. If the total number of customers that bought the game in one day was 156 and the total profit of the company on that day was $9684, which of the following systems of equations could be used to find the number of clients who bought a standard game, 𝑏, and the number who bought a deluxe game, 𝑑, assuming that no one bought more than one game. [A] {𝑏 + 𝑑 = 156 and 55.50 𝑏 + 64.50 𝑑 = 9684 [B] {2(𝑏 + 𝑑) = 156 and 55.50 𝑏 + 64.50 𝑑 = 9684 [C] {𝑏 + 𝑑 = 9684 and 55.50𝑏 + 64.50𝑑 = 156 [D] {2(𝑏 + 𝑑) = 9684 and 55.50 𝑏 + 64.50 𝑑 = 156

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Video Transcript

A video game company released a new game with two versions, a standard version and a deluxe one. The standard version costs 55 dollars and 50 cents and the deluxe one costs 64 dollars and 50 cents. If the total number of customers that bought the game in one day was 156 and the total profit of the company on that day was 9684. Which of the following systems of equations could be used to find the number of clients who bought a standard game, 𝑏, and the number who bought a deluxe game, 𝑑, assuming that no one bought more than one game? A) 𝑏 plus 𝑑 equals 156 and 55.50 times 𝑏 plus 64.50 times 𝑑 equals 9684. B) Two times 𝑏 plus 𝑑 equals 156 and 55.50 times 𝑏 plus 64.50 times 𝑑 equals 9684. C) 𝑏 plus 𝑑 equals 9684 and 55.50𝑏 plus 64.50𝑑 equals 156. And finally, D) two times 𝑏 plus 𝑑 equals 9684 and 55.50 times 𝑏 plus 64.50 times 𝑑 equals 156.

The key here is to identify what these variables represent. Variable 𝑏 represents the number of clients who bought a standard game and variable 𝑑 the number who bought a deluxe game. The total number of customers was 156. And the total number of customers is 𝑏 and 𝑑, the number of customers that bought a standard game and the number of customers who bought a deluxe game. We know that 𝑏 plus 𝑑 must equal 156. Option C has 𝑏 plus 𝑑 equals 9684. This statement would mean that the number of clients who bought a standard game plus the number of clients who bought a deluxe game would equal 9684. So this is not an option.

We have a similar problem with option D. We have two times 𝑏 plus 𝑑 equals 9684. We think this is not correct. But just to make sure, we divide both sides of the equation by two. And then we would see that 𝑏 plus 𝑑 would have to be equal to 9684 divided by two which is 4842. And the total number of customers was not 4842, so D also would not work. With option B we again have this two times 𝑏 plus 𝑑. But this time, it’s equal to 156. If we want to find out what 𝑏 plus 𝑑 is equal to, we would need to divide both sides of the equation by two. 156 divided by two equals 78. And 𝑏 plus 𝑑 equals 78 is saying that the number of customers in total would be 78. And we know that the total number of customers was 156 which is what we see in option A. 𝑏 plus 𝑑 equals 156.

We can also check the second equation in option A which says 55.50 times 𝑏 plus 64.50 times 𝑑 equals 9684. Since 𝑏 represents the number of people who bought the standard game and 55.50 is the cost of the standard game, we would multiply those two values together to get how much money was made from the purchase of the standard game. And then we would see that 64.50 is the cost of the deluxe game. And the variable 𝑑 is the number of people who bought the deluxe game. We multiply those two values together to see how much money was made from the selling of the deluxe game and then add those two values together to get the total profit for the company, 9684. You could use the systems of equations in option A to find out the number of customers who bought the standard game and the number of customers who bought the deluxe game.

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