{"id":"cb_question_bank:0bcd05a7-46db-4786-891d-1566e2ebe64b","source_id":"cb_question_bank","source_item_id":"0bcd05a7-46db-4786-891d-1566e2ebe64b","external_id":null,"ibn":"08086-DC","question_id":"b86123af","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":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price, in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if <span class=\"italic\">x</span> represents the price, in dollars, of each shirt and <span class=\"italic\">y</span> represents the price, in dollars, of each pair of pants?</p>\n","rationale_html":"<p>Choice A is correct. Hiro purchased 4 shirts&nbsp;and each shirt cost <span class=\"italic\">x</span>&nbsp;dollars, so he&nbsp;spent a&nbsp;total of&nbsp;4<span class=\"italic\">x</span>&nbsp;dollars on shirts. Likewise, Hiro purchased 2 pairs of pants, and each pair of pants cost <span class=\"italic\">y</span>&nbsp;dollars, so he&nbsp;spent a total of 2<span class=\"italic\">y</span>&nbsp;dollars on pants. Therefore, the total amount that Hiro spent&nbsp;was 4<span class=\"italic\">x</span> + 2<span class=\"italic\">y</span>. Since Hiro spent $86 in total, this can be modeled by the equation 4<span class=\"italic\">x</span> + 2<span class=\"italic\">y</span> = 86. Using the same reasoning, Sofia bought 3 shirts at <span class=\"italic\">x</span>&nbsp;dollars each and 5 pairs of pants at <span class=\"italic\">y</span>&nbsp;dollars each, so she spent a total of&nbsp;3<span class=\"italic\">x</span> + 5<span class=\"italic\">y</span>&nbsp;dollars on shirts and pants. Since Sofia spent $166 in total, this can be modeled by the equation 3<span class=\"italic\">x</span> + 5<span class=\"italic\">y</span> = 166.</p><p>Choice B is incorrect and may be the result of switching the number of&nbsp;shirts Sofia purchased with the number of pairs of pants Hiro purchased. Choice C is incorrect and may be the result of switching&nbsp;the total price each person paid. Choice D is incorrect and may be the result of switching&nbsp;the total price each person paid as well as switching the number of shirts Sofia purchased with the number of pairs of pants Hiro purchased.</p><p></p>\n","correct_answer":["A"],"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/82c3938d6ad91603c2038c8b2794043d09ac407d34d2f201883a0ae4853c8462\" alt=\"4 x plus 2 y, equals 86, \nand, \n3 x plus 5 y, equals 166\"></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/45a85b2a961647a586c17b654b07c826983394a7afd2b61b4414d35a74f8ea2a\" alt=\"4 x plus 3 y, equals 86, \nand, \n2 x plus 5 y, equals 166\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/29163f6d9911610a0ba27a17677e3d468295f92f95b8f79d9d35a633f29dfcce\" alt=\"4 x plus 2 y, equals 166, \nand, \n3 x plus 5 y, equals 86\"></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/118d862fc4ee662155262f5133b37f482d49308dbce4e5220abd052c07285dc6\" alt=\"4 x plus 3 y, equals 166, \nand, \n2 x plus 5 y, equals 86\"></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}}