{"id":"cb_question_bank:ea891585-d4b7-4f92-a353-78c83fd8a951","source_id":"cb_question_bank","source_item_id":"ea891585-d4b7-4f92-a353-78c83fd8a951","external_id":null,"ibn":"09904-DC","question_id":"7d89376f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A discount airline sells a certain number of tickets, x , for a flight for $90 each. It sells the number of remaining tickets, y , for $250 each. For a particular flight, the airline sold 120 tickets and collected a total of $27,600 from the sale of those tickets. Which system of equations represents this relationship between x and y ?","stimulus":"","stimulus_html":null,"stem_html":"

\n A discount airline sells a certain number of tickets, x, for a flight for $90 each. It sells the number of remaining tickets, y, for $250 each. For a particular flight, the airline sold 120 tickets and collected a total of $27,600 from the sale of those tickets. Which system of equations represents this relationship between x and y ?\n

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Choice A is correct. The airline sold two types of tickets for this flight: x tickets at $90 each and the remaining  tickets, y, at $250 each. Because the airline sold a total of 120 tickets for this flight, it must be true that x + y = 120. The amount, in dollars, collected from the sale of x tickets at $90 each is represented by 90x. The amount, in dollars, collected from the sale of the remaining y tickets at $250 each is represented by 250y. It is given that a total of $27,600 was collected from the sale of all tickets. Therefore, it must also be true that 90x + 250y = 27,600.

Choice B is incorrect. The total number of tickets sold is represented correctly as x + y = 120. The total amount, in dollars, collected from the sale of the x tickets at $90 each and the remaining tickets, y, at $250 has been correctly represented as 90x + 250y. However, according to the information given, this total should be equal to 27,600, not 120(27,600) dollars. Choice C is incorrect. The total number of tickets sold has been correctly represented as x + y. However, according to the information given, this total should be equal to 120, not 27,600, as shown in choice C. The total amount, in dollars, collected from the sale of the x tickets at $90 each and the remaining tickets, y, at $250 has been correctly represented as 90x + 250y. However, according to the information given, this total should be equal to 27,600, not 120(27,600) dollars. Choice D is incorrect. The two equations given in choice D have no meaning in this context.

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