{"id":"cb_question_bank:06868720-2332-4e01-b188-4f2342bc60a9","source_id":"cb_question_bank","source_item_id":"06868720-2332-4e01-b188-4f2342bc60a9","external_id":"07aee0d5-9ae6-4612-bbac-cad96d3eb3dd","ibn":null,"question_id":"88e13c8c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The total cost f left parenthesis x right parenthesis , in dollars, to lease a car for 36 months from a particular car dealership is given by f left parenthesis x right parenthesis equals 36 x plus 1,000 , where x is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is dollar sign 400 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The total cost <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, in dollars, to lease a car for <math alttext=\"36\"><mn>36</mn>\n</math> months from a particular car dealership is given by <math alttext=\"f left parenthesis x right parenthesis equals 36 x plus 1,000\"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mrow><mn>36</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>1,000</mn></mrow></math>, where <math alttext=\"x\"><mi>x</mi>\n</math> is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is <math alttext=\"dollar sign 400\"><mo>$</mo><mrow><mn>400</mn></mrow></math>?</p>","rationale_html":"<p>Choice C is correct. It's given that <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> is the total cost, in dollars, to lease a car from this dealership with a monthly payment of <math alttext=\"x\"><mi>x</mi>\n</math> dollars. Therefore, the total cost, in dollars, to lease the car when the monthly payment is <math alttext=\"dollar sign 400\"><mo>$</mo><mn>400</mn></math> is represented by the value of <math alttext=\"f left parenthesis x right parenthesis\"><mi>f</mi><mfenced><mi>x</mi></mfenced></math> when <math alttext=\"x equals 400\"><mi>x</mi><mo>=</mo><mn>400</mn></math>. Substituting <math alttext=\"400\"><mn>400</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the equation <math alttext=\"f left parenthesis x right parenthesis equals 36 x plus 1,000\"><mi>f</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mn>36</mn><mi>x</mi><mo>+</mo><mn>1,000</mn></math> yields <math alttext=\"f left parenthesis 400 right parenthesis equals 36 left parenthesis 400 right parenthesis plus 1,000\"><mo>&nbsp;</mo><mi>f</mi><mfenced><mn>400</mn></mfenced><mo>=</mo><mn>36</mn><mfenced><mn>400</mn></mfenced><mo>+</mo><mn>1,000</mn></math>, or <math alttext=\"f left parenthesis 400 right parenthesis equals 15,400\"><mi>f</mi><mfenced><mn>400</mn></mfenced><mo>=</mo><mn>15,400</mn></math>. Thus, when the monthly payment is <math alttext=\"dollar sign 400\"><mo>$</mo><mn>400</mn></math>, the total cost to lease a car is&nbsp;<math alttext=\"dollar sign 15,400\"><mo>$</mo><mn>15,400</mn></math>.&nbsp;</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.812000+00:00","source_updated_at":"2023-08-02T20:25:59.812000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"dollar sign 13,400\"><mo>$</mo><mn>13,400</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"dollar sign 13,000\"><mo>$</mo><mn>13,000</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"dollar sign 15,400\"><mo>$</mo><mn>15,400</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"dollar sign 37,400\"><mo>$</mo><mrow><mn>37,400</mn></mrow></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}}