{"id":"cb_question_bank:27a300b4-2208-4b27-8b44-d90327612ea3","source_id":"cb_question_bank","source_item_id":"27a300b4-2208-4b27-8b44-d90327612ea3","external_id":"e3cbd1d8-7084-48db-a4b9-384e8121846d","ibn":null,"question_id":"ff2c1431","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":"7 m equals 5 left parenthesis n plus p right parenthesis The given equation relates the positive numbers m , n , and p . Which equation correctly gives n in terms of m and p ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"7 m equals 5 left parenthesis n plus p right parenthesis\"><mrow><mn>7</mn></mrow><mi>m</mi><mo>=</mo><mrow><mn>5</mn></mrow><mfenced><mrow><mi>n</mi><mo>+</mo><mi>p</mi></mrow></mfenced></math></p>\n<p style=\"text-align: left;\">The given equation relates the positive numbers <math alttext=\"m\"><mi>m</mi>\n</math>, <math alttext=\"n\"><mi>n</mi>\n</math>, and <math alttext=\"p\"><mi>p</mi>\n</math>. Which equation correctly gives <math alttext=\"n\"><mi>n</mi>\n</math> in terms of <math alttext=\"m\"><mi>m</mi>\n</math> and <math alttext=\"p\"><mi>p</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It's given that the equation <math alttext=\"7 m equals 5 left parenthesis n plus p right parenthesis\"><mn>7</mn><mi>m</mi><mo>=</mo><mn>5</mn><mfenced><mrow><mi>n</mi><mo>+</mo><mi>p</mi></mrow></mfenced></math> relates the positive numbers <math alttext=\"m\"><mi>m</mi>\n</math>, <math alttext=\"n\"><mi>n</mi>\n</math>, and <math alttext=\"p\"><mi>p</mi>\n</math>. Dividing both sides of the given equation by <math alttext=\"5\"><mn>5</mn>\n</math> yields <math alttext=\"StartFraction 7 m Over 5 EndFraction equals n plus p\"><mfrac><mrow><mn>7</mn><mi>m</mi></mrow><mn>5</mn></mfrac><mo>=</mo><mi>n</mi><mo>+</mo><mi>p</mi></math>. Subtracting <math alttext=\"p\"><mi>p</mi>\n</math> from both sides of this equation yields <math alttext=\"StartFraction 7 m Over 5 EndFraction minus p equals n\"><mfrac><mrow><mn>7</mn><mi>m</mi></mrow><mn>5</mn></mfrac><mo>-</mo><mi>p</mi><mo>=</mo><mi>n</mi></math>, or <math alttext=\"n equals StartFraction 7 m Over 5 EndFraction minus p\"><mi>n</mi><mo>=</mo><mfrac><mrow><mn>7</mn><mi>m</mi></mrow><mn>5</mn></mfrac><mo>-</mo><mi>p</mi></math>. It follows that the equation <math alttext=\"n equals StartFraction 7 m Over 5 EndFraction minus p\"><mi>n</mi><mo>=</mo><mfrac><mrow><mn>7</mn><mi>m</mi></mrow><mn>5</mn></mfrac><mo>-</mo><mi>p</mi></math> correctly gives <math alttext=\"n\"><mi>n</mi>\n</math> in terms of <math alttext=\"m\"><mi>m</mi>\n</math> and <math alttext=\"p\"><mi>p</mi>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.825000+00:00","source_updated_at":"2023-08-02T20:25:59.825000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"n equals StartFraction 5 p Over 7 m EndFraction\"><mi>n</mi><mo>=</mo><mfrac><mrow><mrow><mn>5</mn></mrow><mi>p</mi></mrow><mrow><mrow><mn>7</mn></mrow><mi>m</mi></mrow></mfrac></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"n equals StartFraction 7 m Over 5 EndFraction minus p\"><mi>n</mi><mo>=</mo><mfrac><mrow><mrow><mn>7</mn></mrow><mi>m</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>-</mo><mi>p</mi></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"n equals 5 left parenthesis 7 m right parenthesis plus p\"><mi>n</mi><mo>=</mo><mrow><mn>5</mn></mrow><mfenced><mrow><mrow><mn>7</mn></mrow><mi>m</mi></mrow></mfenced><mo>+</mo><mi>p</mi></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"n equals 7 m minus 5 minus p\"><mi>n</mi><mo>=</mo><mrow><mn>7</mn></mrow><mi>m</mi><mo>-</mo><mrow><mn>5</mn></mrow><mo>-</mo><mi>p</mi></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}}