{"id":"cb_question_bank:895dfd07-b2d7-49f8-983f-89c4b82f6599","source_id":"cb_question_bank","source_item_id":"895dfd07-b2d7-49f8-983f-89c4b82f6599","external_id":"5041d89b-afb9-486c-83f0-f085fe47f197","ibn":null,"question_id":"8f65cddc","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"StartFraction 1 Over 7 b EndFraction equals StartFraction 11 x Over y EndFraction The given equation relates the positive numbers b , x , and y . Which equation correctly expresses x in terms of b and y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"StartFraction 1 Over 7 b EndFraction equals StartFraction 11 x Over y EndFraction\"><mfrac><mn>1</mn><mrow><mrow><mn>7</mn></mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mrow><mn>11</mn></mrow><mi>x</mi></mrow><mi>y</mi></mfrac></math></p>\n<p>The given equation relates the positive numbers <math alttext=\"b\"><mi>b</mi>\n</math>, <math alttext=\"x\"><mi>x</mi>\n</math>, and <math alttext=\"y\"><mi>y</mi>\n</math>. Which equation correctly expresses <math alttext=\"x\"><mi>x</mi>\n</math> in terms of <math alttext=\"b\"><mi>b</mi>\n</math> and <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p>Choice C is correct. Multiplying each side of the given equation by <math alttext=\"y\"><mi>y</mi>\n</math> yields the equivalent equation <math alttext=\"StartFraction y Over 7 b EndFraction equals 11 x\"><mfrac><mi>y</mi><mrow><mn>7</mn><mi>b</mi></mrow></mfrac><mo>=</mo><mn>11</mn><mi>x</mi></math>. Dividing each side of this equation by <math alttext=\"11\"><mn>11</mn>\n</math> yields <math alttext=\"StartFraction y Over 77 b EndFraction equals x\"><mfrac><mi>y</mi><mrow><mn>77</mn><mi>b</mi></mrow></mfrac><mo>=</mo><mi>x</mi></math>, or&nbsp;<math alttext=\"x equals StartFraction y Over 77 b EndFraction\"><mi>x</mi><mo>=</mo><mfrac><mi>y</mi><mrow><mn>77</mn><mi>b</mi></mrow></mfrac></math>.</p>\n<p>Choice A is incorrect. This equation is not equivalent to the given equation.&nbsp;</p>\n<p>Choice B is incorrect. This equation is not equivalent to the given equation.&nbsp;</p>\n<p>Choice D is incorrect. This equation is not equivalent to the given equation.&nbsp;</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"x equals StartFraction 7 b y Over 11 EndFraction\"><mi>x</mi><mo>=</mo><mfrac><mrow><mrow><mn>7</mn></mrow><mi>b</mi><mi>y</mi></mrow><mrow><mn>11</mn></mrow></mfrac></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"x equals y minus 77 b\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mi>y</mi>\n\t\t<mo>-</mo>\n\t\t<mrow>\n\t\t\t<mn>77</mn>\n\t\t\t<mi>b</mi>\n\t\t</mrow>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"x equals StartFraction y Over 77 b EndFraction\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>y</mi>\n\t\t\t<mrow>\n\t\t\t\t<mn>77</mn>\n\t\t\t\t<mi>b</mi>\n\t\t\t</mrow>\n\t\t</mfrac>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"x equals 77 b y\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>77</mn>\n\t\t<mi>b</mi>\n\t\t<mi>y</mi>\n\t</mrow>\n</mrow>\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}}