{"id":"cb_question_bank:763a85e3-b74c-47ea-9d00-2ff1ea87616b","source_id":"cb_question_bank","source_item_id":"763a85e3-b74c-47ea-9d00-2ff1ea87616b","external_id":null,"ibn":"04476-DC","question_id":"c5082ce3","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40&nbsp;questions and obtained a score of 50, how many questions did the player answer correctly?</p>\n","rationale_html":"<p>The correct answer is 30. Let <span class=\"italic\">x</span> represent the number of correct answers from the player and <span class=\"italic\">y</span> represent the number of incorrect answers from the player. Since the player answered 40 questions in total, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fa10b39c823141fd0c6e5458a948dad8b8def31bd2518dc20dedb8b296631179\" alt=\"x plus y, equals 40\"></span> represents this situation. Also, since the score is found by subtracting the number of incorrect answers from twice the number of correct answers and the player received a score of 50, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1202f984cb3ddd6e1f5ae0c8c1e47c2b5073fab1e4f34e989bc5b6df9c96d29b\" alt=\"2 x minus y, equals 50\"></span> represents this situation. Adding the equations in the system of two equations together yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/596e447b1270d56ff3202ce5a653c10816bf4d0c1096348b53089d66a1dcc888\" alt=\"open parenthesis, x plus y, close parenthesis, plus, open parenthesis, 2 x minus y, close parenthesis, equals, 40 plus 50\"></span>. This can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/68a98587b96e3168038ff6e1cdc7274ef4662e750de26ab0fd65d391553bc9eb\" alt=\"3 x equals 90\"></span>. Finally, solving for <span class=\"italic\">x</span> by dividing both sides of the equation by 3 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b4bfe036194e30a72383121d0c810dfa70f4a6ba134fe4dd0eb864bbcc63a43e\" alt=\"x equals 30\"></span>.<br></p>\n","correct_answer":["30"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[],"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}}