{"id":"cb_question_bank:8146c636-920b-453a-99a5-52a6c33d63d4","source_id":"cb_question_bank","source_item_id":"8146c636-920b-453a-99a5-52a6c33d63d4","external_id":null,"ibn":"05414-DC","question_id":"789975b7","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A gardener buys two kinds of fertilizer. Fertilizer&nbsp;A contains 60%&nbsp;filler materials by weight and Fertilizer&nbsp;B contains 40%&nbsp;filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240&nbsp;pounds of filler materials. Which equation models this relationship, where <span class=\"italic\">x</span> is the number of pounds of Fertilizer&nbsp;A and <span class=\"italic\">y</span> is the number of pounds of Fertilizer&nbsp;B?</p>\n","rationale_html":"<p>Choice B is correct. Since Fertilizer A contains 60% filler materials by weight, it follows that <span class=\"italic\">x</span> pounds of Fertilizer A consists of 0.6<span class=\"italic\">x</span> pounds of filler materials. Similarly, <span class=\"italic\">y</span> pounds of Fertilizer B consists of 0.4<span class=\"italic\">y</span> pounds of filler materials. When <span class=\"italic\">x</span> pounds of Fertilizer A and <span class=\"italic\">y</span> pounds of Fertilizer B are combined, the result is 240 pounds of filler materials. Therefore, the total amount, in pounds, of filler materials in a mixture of <span class=\"italic\">x</span> pounds of Fertilizer A and <span class=\"italic\">y</span> pounds of Fertilizer B can be expressed as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98e4b299dbcdb4903c1d33778bc3562edd4e1945e10652d6d16e17a4e55bec7c\" alt=\"0 point 6 x, plus 0 point 4 y, equals 240\"></span>.</p><p>Choice A is incorrect. This choice transposes the percentages of filler materials for Fertilizer A and Fertilizer B. Fertilizer A consists of 0.6<span class=\"italic\">x</span> pounds of filler materials and Fertilizer B consists of 0.4<span class=\"italic\">y</span> pounds of filler materials. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6a4ad757af4eccd56befd7edc420a130ae06211b89564acebfb2987128a85391\" alt=\"0 point 6 x, plus 0 point 4 y\"></span> is equal to 240, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/91feba2ca11ef415313864c116d86ca12eb0ccb018a1baaa59cda425e0dee1cb\" alt=\"0 point 4 x, plus 0 point 6 y\"></span>. Choice C is incorrect. This choice transposes the percentages of filler materials for Fertilizer A and Fertilizer B and incorrectly represents how to take the percentage of a value mathematically. Choice D is incorrect. This choice incorrectly represents how to take the percentage of a value mathematically. Fertilizer A consists of 0.6<span class=\"italic\">x</span> pounds of filler materials, not 60<span class=\"italic\">x</span> pounds of filler materials, and Fertilizer B consists of 0.4<span class=\"italic\">y</span> pounds of filler materials, not 40<span class=\"italic\">y</span> pounds of filler materials.</p><p>\n        \n      </p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+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/f065c0403e7fe933b8ad6a0a51548c20fe7b3cef06b339e98682290ec165affa\" alt=\"zero point 4 x, plus zero point 6 y, equals 240\"></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/1be88620e798022751190a8576ae493b4991a05b6dc2551b0ef5789d115087b6\" alt=\"zero point 6 x, plus zero point 4 y, equals 240\"></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/9d17181bc19d9466221856e7a812f524b0bd722f2d2e881d924ee65a9586645b\" alt=\"40 x, plus, 60 y, equals 240\"></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/221360589423f941aa17f437c2d9c64f7f812a1aa3ffd51d0722c16cee024114\" alt=\"60 x, plus 40 y, equals 240\"></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}}