{"id":"cb_question_bank:e3571810-6e3a-4189-b0c7-fab01a1d1825","source_id":"cb_question_bank","source_item_id":"e3571810-6e3a-4189-b0c7-fab01a1d1825","external_id":null,"ibn":"10239-DC","question_id":"0df106df","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":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $20, how many novels did she purchase?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">An online bookstore sells novels and magazines. Each novel sells for $4, and each magazine sells for $1. If Sadie purchased a total of 11&nbsp;novels and magazines that have a combined selling price of $20, how many novels did she purchase?</p>\n","rationale_html":"<p>Choice B is correct. Let <span class=\"italic\">n</span> be the number of novels and <em>m </em>be the number of magazines that Sadie purchased. If Sadie purchased a total of 11 novels and magazines, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e63f8f6e3b0dacd12ee5e7a15baa330a551f6c1cc765c87093a899683001c075\" alt=\"n plus m, equals 11\"></span>. It is given that the combined price of 11 novels and magazines is $20. Since each novel sells for $4 and each magazine sells for $1, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/89e3d7d5c6a405d8c42e24aaa230c68a5cc0d70421cd159e9c70b3848e964b90\" alt=\"4 n plus m, equals 20\"></span>. So the system of equations below must hold.</p><p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0ea16263eb4a666902aa8b3ef885232e7b6343bf1cd8c118d421624d4c748f3\" alt=\"4 n plus m, equals 20; n plus m, equals 11\"></span></p><p>Subtracting corresponding sides of the second equation from the first equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7898cfdd49098921c4de18e03f1d189ba12241fb0ad5b3fe36fb057f455a358d\" alt=\"3 n equals 9\"></span>,&nbsp;so <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1dd8cbfd0011902f4c97f5669c17d20f7ca7825001e960d1a99b5cc23d7f8a26\" alt=\"n equals 3\"></span>. Therefore, Sadie purchased 3 novels.</p><p>Choice A is incorrect. If 2 novels were purchased, then a total of $8 was spent on novels. That leaves $12 to be spent on magazines, which means that 12 magazines would have been purchased. However, Sadie purchased a total of 11 novels and magazines. Choices C and D are incorrect. If 4 novels were purchased, then a total of $16 was spent on novels. That leaves $4 to be spent on magazines, which means that 4 magazines would have been purchased. By the same logic, if Sadie purchased 5 novels, she would have no money at all ($0) to buy magazines. However, Sadie purchased a total of 11 novels and magazines.</p><p>&nbsp;</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p>2</p>\n","ord":0},{"label":"B","content_html":"<p>3</p>\n","ord":1},{"label":"C","content_html":"<p>4</p>\n","ord":2},{"label":"D","content_html":"<p>5</p>\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}}