{"id":"cb_question_bank:ef1e44e3-37ba-4af0-b358-1509055b9aa0","source_id":"cb_question_bank","source_item_id":"ef1e44e3-37ba-4af0-b358-1509055b9aa0","external_id":"4959c26d-16dc-4df2-8bb7-92bd72d87aa5","ibn":null,"question_id":"bbf9e5ce","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For groups of 25 or more people, a museum charges dollar sign 21 per person for the first 25 people and dollar sign 14 for each additional person. Which function f gives the total charge, in dollars, for a tour group with n people, where n greater than or equals 25 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">For groups of <math alttext=\"25\"><mn>25</mn>\n</math> or more people, a museum charges <math alttext=\"dollar sign 21\"><mo>$</mo><mn>21</mn>\n</math> per person for the first <math alttext=\"25\"><mn>25</mn>\n</math> people and <math alttext=\"dollar sign 14\"><mo>$</mo><mn>14</mn>\n</math> for each additional person. Which function <math alttext=\"f\"><mi>f</mi>\n</math> gives the total charge, in dollars, for a tour group with <math alttext=\"n\"><mi>n</mi>\n</math> people, where <math alttext=\"n greater than or equals 25\"><mi>n</mi><mo>≥</mo><mn>25</mn></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. A tour group with <math alttext=\"n\"><mi>n</mi>\n</math> people, where <math alttext=\"n greater than or equals 25\"><mi>n</mi><mo>≥</mo><mn>25</mn></math>, can be split into two subgroups: the first <math alttext=\"25\"><mn>25</mn>\n</math> people and the additional <math alttext=\"n minus 25\"><mrow>\n\t<mi>n</mi>\n\t<mo>-</mo>\n\t<mn>25</mn>\n</mrow>\n</math> people. Since the museum charges <math alttext=\"dollar sign 21\"><mo>$</mo><mn>21</mn></math> per person for the first <math alttext=\"25\"><mn>25</mn>\n</math> people and <math alttext=\"dollar sign 14\"><mo>$</mo><mn>14</mn></math> for each additional person, the charge for the first <math alttext=\"25\"><mn>25</mn>\n</math> people is <math alttext=\"dollar sign 21 left parenthesis 25 right parenthesis\"><mo>$</mo><mn>21</mn><mo>(</mo><mn>25</mn><mo>)</mo></math> and the charge for the additional <math alttext=\"n minus 25\"><mrow>\n\t<mi>n</mi>\n\t<mo>-</mo>\n\t<mn>25</mn>\n</mrow>\n</math> people is <math alttext=\"dollar sign 14 left parenthesis n minus 25 right parenthesis\"><mo>$</mo><mn>14</mn><mo>(</mo><mi>n</mi><mo>-</mo><mn>25</mn><mo>)</mo></math>. Therefore, the total charge, in dollars, is given by the function <math alttext=\"f left parenthesis n right parenthesis equals 21 left parenthesis 25 right parenthesis plus 14 left parenthesis n minus 25 right parenthesis\"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>21</mn><mo>(</mo><mn>25</mn><mo>)</mo><mo>+</mo><mn>14</mn><mo>(</mo><mi>n</mi><mo>-</mo><mn>25</mn><mo>)</mo></math>, or <math alttext=\"f left parenthesis n right parenthesis equals 14 n plus 175\"><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>14</mn><mi>n</mi><mo>+</mo><mn>175</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B 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":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.810000+00:00","source_updated_at":"2023-08-02T20:25:59.810000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"f left parenthesis n right parenthesis equals 14 n plus 175\"><mi>f</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>14</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>175</mn>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"f left parenthesis n right parenthesis equals 14 n plus 525\"><mi>f</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>14</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>525</mn>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"f left parenthesis n right parenthesis equals 35 n minus 350\"><mi>f</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>35</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>350</mn>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"f left parenthesis n right parenthesis equals 14 n plus 21\"><mi>f</mi><mfenced><mi>n</mi></mfenced><mo>=</mo><mrow>\n\t<mrow>\n\t\t<mn>14</mn>\n\t\t<mi>n</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>21</mn>\n</mrow>\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}}