{"id":"cb_question_bank:f519630c-3671-4686-9d4b-5d9200090e72","source_id":"cb_question_bank","source_item_id":"f519630c-3671-4686-9d4b-5d9200090e72","external_id":"2b61c753-bb12-4153-963a-865282e1a793","ibn":null,"question_id":"fcb78856","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":"b equals 42 c f The given equation relates the positive numbers b , c , and f . Which equation correctly expresses c in terms of b and f ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"b equals 42 c f\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>42</mn>\n\t\t<mi>c</mi>\n\t\t<mi>f</mi>\n\t</mrow>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">The given equation relates the positive numbers <math alttext=\"b\"><mi>b</mi>\n</math>, <math alttext=\"c\"><mi>c</mi>\n</math>, and <math alttext=\"f\"><mi>f</mi>\n</math>. Which equation correctly expresses <math alttext=\"c\"><mi>c</mi>\n</math> in terms of <math alttext=\"b\"><mi>b</mi>\n</math> and <math alttext=\"f\"><mi>f</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that the equation <math alttext=\"b equals 42 c f\"><mi>b</mi><mo>=</mo><mn>42</mn><mi>c</mi><mi>f</mi></math> relates the positive numbers <math alttext=\"b\"><mi>b</mi>\n</math>, <math alttext=\"c\"><mi>c</mi>\n</math>, and <math alttext=\"f\"><mi>f</mi>\n</math>. Dividing each side of the given equation by <math alttext=\"42 f\"><mrow>\n\t<mn>42</mn>\n\t<mi>f</mi>\n</mrow>\n</math> yields <math alttext=\"StartFraction b Over 42 f EndFraction equals c\"><mfrac><mi>b</mi><mrow><mn>42</mn><mi>f</mi></mrow></mfrac><mo>=</mo><mi>c</mi></math>, or <math alttext=\"c equals StartFraction b Over 42 f EndFraction\"><mi>c</mi><mo>=</mo><mfrac><mi>b</mi><mrow><mn>42</mn><mi>f</mi></mrow></mfrac></math>. Thus, the equation&nbsp;<math alttext=\"c equals StartFraction b Over 42 f EndFraction\"><mi>c</mi><mo>=</mo><mfrac><mi>b</mi><mrow><mn>42</mn><mi>f</mi></mrow></mfrac></math> correctly expresses <math alttext=\"c\"><mi>c</mi>\n</math> in terms of <math alttext=\"b\"><mi>b</mi>\n</math> and <math alttext=\"f\"><mi>f</mi>\n</math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This equation can be rewritten as&nbsp;<math alttext=\"b equals c f plus 42\"><mi>b</mi><mo>=</mo><mi>c</mi><mi>f</mi><mo>+</mo><mn>42</mn></math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This equation can be rewritten as&nbsp;<math alttext=\"b equals StartFraction c Over 42 f EndFraction\"><mi>b</mi><mo>=</mo><mfrac><mi>c</mi><mrow><mn>42</mn><mi>f</mi></mrow></mfrac></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This equation can be rewritten as&nbsp;<math alttext=\"b equals 42 minus c minus f\"><mi>b</mi><mo>=</mo><mn>42</mn><mo>-</mo><mi>c</mi><mo>-</mo><mi>f</mi></math>.</p>","correct_answer":["A"],"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=\"c equals StartFraction b Over 42 f EndFraction\"><mrow>\n\t<mi>c</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>b</mi>\n\t\t\t<mrow>\n\t\t\t\t<mn>42</mn>\n\t\t\t\t<mi>f</mi>\n\t\t\t</mrow>\n\t\t</mfrac>\n\t</mrow>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"c equals StartFraction b minus 42 Over f EndFraction\"><mrow>\n\t<mi>c</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mrow>\n\t\t\t\t<mi>b</mi>\n\t\t\t\t<mo>-</mo>\n\t\t\t\t<mn>42</mn>\n\t\t\t</mrow>\n\t\t\t<mi>f</mi>\n\t\t</mfrac>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"c equals 42 b f\"><mrow>\n\t<mi>c</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>42</mn>\n\t\t<mi>b</mi>\n\t\t<mi>f</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"c equals 42 minus b minus f\"><mi>c</mi><mo>=</mo><mrow><mn>42</mn></mrow><mo>-</mo><mi>b</mi><mo>-</mo><mi>f</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}}