{"id":"cb_question_bank:92294c39-b8c2-4619-a3ee-e927e687ac99","source_id":"cb_question_bank","source_item_id":"92294c39-b8c2-4619-a3ee-e927e687ac99","external_id":"ce40ca76-4f75-4034-9e39-b6c214f31eea","ibn":null,"question_id":"c8fb6bcb","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals 2 x plus 244 The given function f represents the perimeter, in centimeters left parenthesis cm right parenthesis , of a rectangle with a length of x cm and a fixed width. What is the width, in cm , of the rectangle?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"f left parenthesis x right parenthesis equals 2 x plus 244\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mrow><mn>244</mn></mrow></math></p>\n<p style=\"text-align: left;\">The given function <math alttext=\"f\"><mi>f</mi>\n</math> represents the perimeter, in <math alttext=\"centimeters left parenthesis cm right parenthesis\"><mtext>centimeters</mtext><mo>&nbsp;</mo><mfenced><mtext>cm</mtext></mfenced></math>, of a rectangle with a length of <math alttext=\"x cm\"><mi>x</mi><mo>&nbsp;</mo><mtext>cm</mtext></math> and a fixed width. What is the width, in <math alttext=\"cm\"><mtext>cm</mtext></math>, of the rectangle?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It's given that <math alttext=\"f left parenthesis x right parenthesis equals 2 x plus 244\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>244</mn></math> represents the perimeter, in <math alttext=\"centimeters left parenthesis cm right parenthesis\"><mtext>centimeters</mtext><mo>&nbsp;</mo><mo>(</mo><mtext>cm</mtext><mo>)</mo></math>, of a rectangle with a length of <math alttext=\"x\"><mi>x</mi>\n</math>&nbsp;<math alttext=\"c m\"><mi>cm</mi></math> and a fixed width. If <math alttext=\"w\"><mi>w</mi>\n</math> represents a fixed width, in <math alttext=\"cm\"><mtext>cm</mtext></math>, then the perimeter, in <math alttext=\"cm\"><mtext>cm</mtext></math>, of a rectangle with a length of <math alttext=\"x\"><mi>x</mi>\n</math> <math alttext=\"cm\"><mtext>cm</mtext></math> and a fixed width of <math alttext=\"w\"><mi>w</mi>\n</math> <math alttext=\"cm\"><mtext>cm</mtext></math> can be given by the function <math alttext=\"f left parenthesis x right parenthesis equals 2 x plus 2 w\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>w</mi></math>. Therefore, <math alttext=\"2 x plus 2 w equals 2 x plus 244\"><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>w</mi><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>244</mn></math>. Subtracting <math alttext=\"2 x\"><mrow>\n\t<mn>2</mn>\n\t<mi>x</mi>\n</mrow>\n</math> from both sides of this equation yields <math alttext=\"2 w equals 244\"><mn>2</mn><mi>w</mi><mo>=</mo><mn>244</mn></math>. Dividing both sides of this equation by <math alttext=\"2\"><mn>2</mn>\n</math> yields <math alttext=\"w equals 122\"><mi>w</mi><mo>=</mo><mn>122</mn></math>. Therefore, the width, in <math alttext=\"cm\"><mtext>cm</mtext></math>, of the rectangle is <math alttext=\"122\"><mn>122</mn>\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":"2023-08-02T20:25:59.811000+00:00","source_updated_at":"2023-08-02T20:25:59.811000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"2\"><mn>2</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"122\"><mn>122</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"244\"><mn>244</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"488\"><mn>488</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}}