{"id":"cb_question_bank:ed92777d-a542-4eb0-8dab-b4a6177f1b77","source_id":"cb_question_bank","source_item_id":"ed92777d-a542-4eb0-8dab-b4a6177f1b77","external_id":null,"ibn":"07542-DC","question_id":"17f176ec","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 movie theater charges $11 for each full-price ticket and $8.25 for each reduced-price ticket. For one movie showing, the theater sold a total of 214 full-price and reduced-price tickets for $2,145. Which of the following systems of equations could be used to determine the number of full-price tickets, f , and the number of reduced-price tickets, r , sold?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A movie theater charges $11 for each full-price ticket and $8.25 for each reduced-price ticket. For one movie showing, the theater sold a total of 214&nbsp;full-price and reduced-price tickets for $2,145. Which of the following systems of equations could be used to determine the number of full-price tickets, <span class=\"italic\">f</span>, and the number of reduced-price tickets, <span class=\"italic\">r</span>, sold?</p>\n","rationale_html":"<p>Choice B is correct. The movie theater sells <span class=\"italic\">f</span> full-price tickets and <span class=\"italic\">r</span> reduced-price tickets, so the total number of tickets sold is <span class=\"italic\">f</span> + <span class=\"italic\">r</span>. Since the movie theater sold a total of 214 full-price and reduced-price tickets for one movie showing, it follows that<span class=\"italic\"> f</span> + <span class=\"italic\">r</span> = 214. The movie theater charges $11 for each full-price ticket; thus, the sales for full-price tickets, in dollars, is given by 11<span class=\"italic\">f</span>. The movie theater charges $8.25 for each reduced-price ticket; thus, the sales for reduced-price tickets, in dollars, is given by 8.25<span class=\"italic\">r</span>. Therefore, the total sales, in dollars, for the movie showing is given by 11<span class=\"italic\">f</span> + 8.25<span class=\"italic\">r</span>. Since the total sales for all full-price and reduced-price tickets is $2,145, it follows that 11<span class=\"italic\">f</span> + 8.25<span class=\"italic\">r</span> = 2,145.</p><p>Choice A is incorrect. This system of equations suggests that the movie theater sold a total of 2,145 full-price and reduced-price tickets for a total of $214. Choice C is incorrect. This system suggests that the movie theater charges $8.25 for each full-price ticket and $11 for each reduced-price ticket. Choice D is incorrect. This system suggests that the movie theater charges $8.25 for each full-price ticket and $11 for each reduced-price ticket and sold a total of 2,145 tickets for a total of $214.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.633000+00:00","source_updated_at":"2023-08-02T20:25:59.633000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/48d8a972fd87e4d801fd4da24b09021b4f7dff56c9e9e196fb43f9adafb731cb\" alt=\"f plus r, equals 2,145, and, 11 f plus 8 point 2 5 r, equals 214\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/69eb6369b4af6ddb167008213050fe656be1cd1cd989db1fa56948f9025ca7af\" alt=\"f plus r, equals 214, and, 11 f plus 8 point 2 5 r, equals 2,145\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f64bd78ee1cf6b85a9977eec89ac8c9366250735d44db5982a6b18b346d17278\" alt=\"f plus r, equals 214, and, 8 point 2 5 f plus 11 r, equals 2,145\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0906a8cb303bb54c34942a67c234dd6e4499d516bcdf4b2a2702398107fd9e30\" alt=\"f plus r, equals 2,145, and, 8 point 2 5 f plus 11 r, equals 214\"></span></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}