{"id":"cb_question_bank:a5a13c7f-f52d-4210-aefd-8474d083ee88","source_id":"cb_question_bank","source_item_id":"a5a13c7f-f52d-4210-aefd-8474d083ee88","external_id":null,"ibn":"08084-DC","question_id":"ee031767","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two 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 dance teacher ordered outfits for students for a dance recital. Outfits for boys cost $26, and outfits for girls cost $35. The dance teacher ordered a total of 28 outfits and spent $881. If b represents the number of outfits the dance teacher ordered for boys and g represents the number of outfits the dance teacher ordered for girls, which of the following systems of equations can be solved to find b and g ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A dance teacher ordered outfits for students for a dance recital. Outfits for boys cost $26, and outfits for girls cost $35. The dance teacher ordered a total of 28 outfits and spent $881. If <span class=\"italic\">b</span> represents the number of outfits the dance teacher ordered for boys and <span class=\"italic\">g</span> represents the number of outfits the dance teacher ordered for girls, which of the following systems of equations can be solved to find <span class=\"italic\">b</span> and <span class=\"italic\">g</span> ?</p>\n","rationale_html":"<p>Choice B is correct. Outfits for boys cost $26 each and the teacher ordered <span class=\"italic\">b</span> outfits for boys, so the teacher spent 26<span class=\"italic\">b</span> dollars on outfits for boys. Similarly, outfits for girls cost $35 each and the teacher ordered <span class=\"italic\">g</span> outfits for girls, so the teacher spent 35<span class=\"italic\">g</span> dollars on outfits for girls. Since the teacher spent a total of $881 on outfits for boys and girls, the equation 26<span class=\"italic\">b</span> + 35<span class=\"italic\">g</span> = 881 must be true. And since the teacher ordered a total of 28 outfits, the equation <span class=\"italic\">b</span> + <span class=\"italic\">g</span> = 28 must also be true.</p><p>\n        <br>\nChoice A is incorrect and may result from switching the constraint on the total number of outfits with the constraint on the cost of the outfits. Choice C is incorrect and may result from switching the constraint on the total number of outfits with the constraint on the cost of the outfits, as well as switching the cost of the outfits for boys with the cost of the outfits for girls. Choice D is incorrect and may result from switching the cost of the outfits for boys with the cost of the outfits for girls.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd26411e539289d2fa2b4cc41c369461f8dca6d5b3ae88ee70b604df5a7bd9c9\" alt=\"Each option consists of two equations. 26 b plus 35 g, equals 28, \nand, b plus g, equals 881\n\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7c886a940c81a2038bc6206a41d46e8c40a9c0cca049d5cb542b1570fa294635\" alt=\"26 b plus 35 g, equals 881, \nand,\nb plus g, equals 28\n\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/825c533314933e09d34cc8da1c5dd7e3215e2185b635212a9eaeb94ec4eaafb3\" alt=\"26 g plus 35 b, equals 28, and, b plus g, equals 881\n\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f2ef7e9b7ab4ec83bf932e8ad3292cd5cc1caf94935b6da78df6b60c7ac92bfe\" alt=\"26 g plus 35 b, equals 881, and, b plus g, equals 28\n\"></span></span>\n          </p>\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}}