{"id":"cb_question_bank:d6d2db22-ca2d-4b0d-b137-43cc6a562d9f","source_id":"cb_question_bank","source_item_id":"d6d2db22-ca2d-4b0d-b137-43cc6a562d9f","external_id":"1ce8eb76-74a1-43fe-a9d0-df147e4ca59e","ibn":null,"question_id":"686b7cad","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A proposal for a new library was included on an election ballot. A radio show stated that <math alttext=\"3\"><mn>3</mn>\n</math> times as many people voted in favor of the proposal as people who voted against it. A social media post reported that <math alttext=\"15,000\"><mn>15,000</mn>\n</math> more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that a radio show stated that <math alttext=\"3\"><mn>3</mn>\n</math> times as many people voted in favor of the proposal as people who voted against it. Let <math alttext=\"x\"><mi>x</mi>\n</math> represent the number of people who voted against the proposal. It follows that <math alttext=\"3 x\"><mrow>\n\t<mn>3</mn>\n\t<mi>x</mi>\n</mrow>\n</math> is the number of people who voted in favor of the proposal and <math alttext=\"3 x minus x\"><mn>3</mn><mi>x</mi><mo>-</mo><mi>x</mi></math>, or <math alttext=\"2 x\"><mrow>\n\t<mn>2</mn>\n\t<mi>x</mi>\n</mrow>\n</math>, is how many more people voted in favor of the proposal than voted against it. It's also given that a social media post reported that <math alttext=\"15,000\"><mn>15,000</mn>\n</math> more people voted in favor of the proposal than voted against it. Thus, <math alttext=\"2 x equals 15,000\"><mn>2</mn><mi>x</mi><mo>=</mo><mn>15,000</mn></math>. Since <math alttext=\"2 x equals 15,000\"><mn>2</mn><mi>x</mi><mo>=</mo><mn>15,000</mn></math>, the value of <math alttext=\"x\"><mi>x</mi>\n</math> must be half of <math alttext=\"15,000\"><mn>15,000</mn>\n</math>, or <math alttext=\"7,500\"><mn>7,500</mn>\n</math>. Therefore, <math alttext=\"7,500\"><mn>7,500</mn>\n</math> people voted against the proposal.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is how many more people voted in favor of the proposal than voted against it, not the number of people who voted against the proposal.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the number of people who voted in favor of the proposal, not the number of people who voted against the proposal.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.816000+00:00","source_updated_at":"2023-08-02T20:25:59.816000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"7,500\"><mn>7,500</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"15,000\"><mn>15,000</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"22,500\"><mn>22,500</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"45,000\"><mn>45,000</mn>\n</math></p>","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}}