{"id":"cb_question_bank:2b64c755-07db-49bd-8c47-29156cd69ba3","source_id":"cb_question_bank","source_item_id":"2b64c755-07db-49bd-8c47-29156cd69ba3","external_id":"be93eda4-1b01-4cb3-9e00-0859362e1713","ibn":null,"question_id":"c50ede6d","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The total cost, in dollars, to rent a surfboard consists of a dollar sign 25 service fee and a dollar sign 10 per hour rental fee. A person rents a surfboard for t hours and intends to spend a maximum of dollar sign 75 to rent the surfboard. Which inequality represents this situation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The total cost, in dollars, to rent a surfboard consists of a <math alttext=\"dollar sign 25\"><mo>$</mo><mn>25</mn>\n</math> service fee and a <math alttext=\"dollar sign 10\"><mo>$</mo><mn>10</mn>\n</math> per hour rental fee. A person rents a surfboard for <math alttext=\"t\"><mi>t</mi>\n</math> hours and intends to spend a maximum of <math alttext=\"dollar sign 75\"><mo>$</mo><mn>75</mn>\n</math> to rent the surfboard. Which inequality represents this situation?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. The cost of the rental fee depends on the number of hours the surfboard is rented. Multiplying <math alttext=\"t\"><mi>t</mi>\n</math> hours by <math alttext=\"10\"><mn>10</mn>\n</math> dollars per hour yields a rental fee of <math alttext=\"10 t\"><mrow>\n\t<mn>10</mn>\n\t<mi>t</mi>\n</mrow>\n</math> dollars. The total cost of the rental consists of the rental fee plus the <math alttext=\"25\"><mn>25</mn>\n</math> dollar service fee, which yields a total cost of <math alttext=\"25 plus 10 t\"><mn>25</mn><mo>+</mo><mn>10</mn><mi>t</mi></math> dollars. Since the person intends to spend a maximum of <math alttext=\"75\"><mn>75</mn>\n</math> dollars to rent the surfboard, the total cost must be at most <math alttext=\"75\"><mn>75</mn>\n</math> dollars. Therefore, the inequality <math alttext=\"25 plus 10 t less than or equals 75\"><mn>25</mn><mo>+</mo><mn>10</mn><mi>t</mi><mo>≤</mo><mn>75</mn></math> represents this situation.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This represents a situation where the rental fee, not the total cost, is at most <math alttext=\"75\"><mn>75</mn>\n</math> dollars.</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>","correct_answer":["D"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"10 t less than or equals 75\"><mn>10</mn><mi>t</mi><mo>≤</mo><mn>75</mn></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10 plus 25 t less than or equals 75\"><mn>10</mn><mo>+</mo><mn>25</mn><mi>t</mi><mo>≤</mo><mn>75</mn></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"25 t less than or equals 75\"><mn>25</mn><mi>t</mi><mo>≤</mo><mn>75</mn></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"25 plus 10 t less than or equals 75\"><mn>25</mn><mo>+</mo><mn>10</mn><mi>t</mi><mo>≤</mo><mn>75</mn></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}}