{"id":"cb_question_bank:75a7b8a9-1452-4ff8-8b41-9bd2e748ced8","source_id":"cb_question_bank","source_item_id":"75a7b8a9-1452-4ff8-8b41-9bd2e748ced8","external_id":"6130d2b7-20eb-4881-8cfa-8ee3adb6499e","ibn":null,"question_id":"b8c4a1cd","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":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"8 j equals k plus 15 m The given equation relates the distinct positive numbers j , k , and m . Which equation correctly expresses j in terms of k and m ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"8 j equals k plus 15 m\"><mrow><mn>8</mn></mrow><mi>j</mi><mo>=</mo><mi>k</mi><mo>+</mo><mrow><mn>15</mn></mrow><mi>m</mi></math></p>\n<p style=\"text-align: left;\">The given equation relates the distinct positive numbers <math alttext=\"j\"><mi>j</mi>\n</math>, <math alttext=\"k\"><mi>k</mi>\n</math>, and <math alttext=\"m\"><mi>m</mi>\n</math>. Which equation correctly expresses <math alttext=\"j\"><mi>j</mi>\n</math> in terms of <math alttext=\"k\"><mi>k</mi>\n</math> and <math alttext=\"m\"><mi>m</mi>\n</math>?</p>","rationale_html":"<p>Choice D is correct. To express <math alttext=\"j\"><mi>j</mi>\n</math> in terms of <math alttext=\"k\"><mi>k</mi>\n</math> and <math alttext=\"m\"><mi>m</mi>\n</math>, the given equation must be solved for <math alttext=\"j\"><mi>j</mi>\n</math>. Dividing each side of the given equation by <math alttext=\"8\"><mn>8</mn>\n</math> yields &nbsp;<math alttext=\"j equals StartFraction k plus 15 m Over 8 EndFraction\"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>+</mo><mn>15</mn><mi>m</mi></mrow><mn>8</mn></mfrac></math>.</p>\n<p>Choice A is incorrect. This is equivalent to <math alttext=\"8 j equals k plus 120 m\"><mn>8</mn><mi>j</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>120</mn><mi>m</mi></math>.</p>\n<p>Choice B is incorrect. This is equivalent to <math alttext=\"8 j equals 8 k plus 15 m\"><mn>8</mn><mi>j</mi><mo>=</mo><mn>8</mn><mi>k</mi><mo>+</mo><mn>15</mn><mi>m</mi></math>.</p>\n<p>Choice C is incorrect. This is equivalent to <math alttext=\"StartFraction j Over 8 EndFraction equals k plus 15 m\"><mfrac><mi>j</mi><mn>8</mn></mfrac><mo>=</mo><mi>k</mi><mo>+</mo><mn>15</mn><mi>m</mi></math>.</p>","correct_answer":["D"],"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=\"j equals StartFraction k Over 8 EndFraction plus 15 m\"><mi>j</mi><mo>=</mo><mfrac><mi>k</mi><mrow><mn>8</mn></mrow></mfrac><mo>+</mo><mrow><mn>15</mn></mrow><mi>m</mi></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"j equals k plus StartFraction 15 m Over 8 EndFraction\"><mi>j</mi><mo>=</mo><mi>k</mi><mo>+</mo><mfrac><mrow><mrow><mn>15</mn></mrow><mi>m</mi></mrow><mrow><mn>8</mn></mrow></mfrac></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"j equals 8 left parenthesis k plus 15 m right parenthesis\"><mi>j</mi><mo>=</mo><mrow><mn>8</mn></mrow><mo>(</mo><mi>k</mi><mo>+</mo><mrow><mn>15</mn></mrow><mi>m</mi><mo>)</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"j equals StartFraction k plus 15 m Over 8 EndFraction\"><mi>j</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>+</mo><mrow><mn>15</mn></mrow><mi>m</mi></mrow><mrow><mn>8</mn></mrow></mfrac></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}}