{"id":"cb_question_bank:3440ae5c-fb31-4fd8-96dc-fb9a5ff0c678","source_id":"cb_question_bank","source_item_id":"3440ae5c-fb31-4fd8-96dc-fb9a5ff0c678","external_id":null,"ibn":"05729-DC","question_id":"95cad55f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300&nbsp;pounds in a shipment. Each container of detergent weighs 7.35 &nbsp;pounds, and each container of fabric softener weighs 6.2&nbsp;pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let <span class=\"italic\">d</span> represent the number of containers of detergent, and let <span class=\"italic\">s</span> represent the number of containers of fabric softener, where <span class=\"italic\">d</span> and <span class=\"italic\">s</span> are nonnegative integers. Which of the following systems of inequalities best represents this situation?</p>\n","rationale_html":"<p>\n        \n      </p><p>Choice A is correct. The number of containers in a shipment must have a weight less than or equal to 300 pounds. The total weight, in pounds, of detergent and fabric softener that the supplier delivers can be expressed as the weight of each container multiplied by the number of each type of container, which is 7.35<span class=\"italic\">d</span> for detergent and 6.2<span class=\"italic\">s</span> for fabric softener. Since this total cannot exceed 300 pounds, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/09978a1806250e4b242b7878b80a9511bc76f4ef293c4f503450040687d4f00e\" alt=\"7 point 3 5 d, plus 6 point 2 s, is less than or equal to 300\"></span>. Also, since the laundry service wants to buy at least twice as many containers of detergent as containers of fabric softener, the number of containers of detergent should be greater than or equal to two times the number of containers of fabric softener. This can be expressed by the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/49a1929a728731c5dee4ba452365be8707124c3659f84f981753a5a09d2ec658\" alt=\"d is greater than or equal to 2 s\"></span>.</p><p>Choice B is incorrect because it misrepresents the relationship between the numbers of each container that the laundry service wants to buy. Choice C is incorrect because the first inequality of the system incorrectly doubles the weight per container of detergent. The weight of each container of detergent is 7.35, not 14.7 pounds. Choice D is incorrect because it doubles the weight per container of detergent and transposes the relationship between the numbers of containers.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a4764e5b34400c40979f99f73608b5fcc7ab450d54d028dfc95d1b8bda46081\" alt=\"7 point three five d, plus, 6 point 2 s, is less than or equal to 300, and, d is greater than or equal to 2 s\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/47ab123f39b4046921706199f27b73fc0d66e55b4cfc7b05abb173718af18e7b\" alt=\"7 point three five d, plus, 6 point 2 s, is less than or equal to 300, and, 2 d is greater than or equal to s\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4f1d9143aba26772ffdc43280d89075a4c47481cb29665cea8695b56aecbdcce\" alt=\"14 point 7 d, plus, 6 point 2 s, is less than or equal to 300, and, d is greater than or equal to 2 s\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/af9f4482996866a420ddcc65d8168a3b2c22eff98faef3aecb187c7bbe0688a2\" alt=\"14 point 7 d, plus, 6 point 2 s, is less than or equal to 300, and, 2 d is greater than or equal to s\"></span></span>\n","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}}