{"id":"cb_question_bank:42aabcd1-bdad-4faa-b8a2-6e43fe33beaf","source_id":"cb_question_bank","source_item_id":"42aabcd1-bdad-4faa-b8a2-6e43fe33beaf","external_id":null,"ibn":"028848-DC","question_id":"181cc4d6","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Rectangle A has length 15 and width w . Rectangle B has length 20 and the same length-to-width ratio as rectangle A . What is the width of rectangle B in terms of w ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Rectangle <span class=\"italic\">A</span> has length 15 and width <span class=\"italic\">w</span>. Rectangle <span class=\"italic\">B</span> has length 20 and the same length-to-width ratio as rectangle <span class=\"italic\">A</span>. What is the width of rectangle <span class=\"italic\">B</span> in terms of&nbsp;<span class=\"italic\">w&nbsp;</span>?</p>\n","rationale_html":"<p>Choice A is correct. It’s given that rectangle <span class=\"italic\">A</span> has length 15 and width <span class=\"italic\">w</span>. Therefore, the length-to-width ratio of rectangle <span class=\"italic\">A</span> is 15 to <span class=\"italic\">w</span>. It’s also given that rectangle <span class=\"italic\">B</span> has length 20 and the same length-to-width ratio as rectangle <span class=\"italic\">A</span>. Let <span class=\"italic\">x</span> represent the width of rectangle <span class=\"italic\">B</span>. The proportion <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f005e9cc0c54fc77b527f3fa8a20f86a3d1d0dd04f80f4b0d45f8ecfe562aee2\" alt=\"15 over w, equals, 20 over x \"></span> can be used to solve for <span class=\"italic\">x</span> in terms of <span class=\"italic\">w</span>. Multiplying both sides of this equation by <span class=\"italic\">x</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e9c3e6ca881a16ae0ba6162eeb2c7fd6d89e3c6123556f94edb00465b1ba1022\" alt=\"the fraction 15 x over w, equals 20\"></span>, and then multiplying both sides of this equation by <span class=\"italic\">w</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d01f907c7c0d96a7cefaeda62bd7d264d9011ebe82f73d2f0f5f44cabce9c2a\" alt=\"15 x equals 20 w\"></span>. Dividing both sides of this equation by 15 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bd225992ee67efafb53891951e722ad930d25022ead9d61ab02def79c98a6844\" alt=\"x equals, the fraction 20 w over 15\"></span>. Simplifying this fraction yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc3bff051c006ec7114fc23875d1bb1760f24141bebc80d19605ae1952d27df4\" alt=\"x equals, four thirds w\"></span>.</p><p>Choices B and D are incorrect and may result from interpreting the difference in the lengths of rectangle <span class=\"italic\">A</span> and rectangle <span class=\"italic\">B</span> as equivalent to the difference in the widths of rectangle <span class=\"italic\">A</span> and rectangle <span class=\"italic\">B</span>. Choice C is incorrect and may result from using a length-to-width ratio of <span class=\"italic\">w</span> to 15, instead of 15 to <span class=\"italic\">w</span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c89e254da60cbb2ed67a016bb878fbda15dfe78c08423588387f222b4d8d3fe4\" alt=\"four-thirds w\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/780a778f31ae0b1eac599f230cd2d1b2d8ac11e11598490f4ae11d05453c66a8\" alt=\"w plus 5\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/26182daafccf16314bb1a047e5c554a541a0803d81f3c8fe89e2a47b1c3bb648\" alt=\"three-fourths w\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc032a82025388224bc610a7912a31e8116dd02503583acd41269cb5dd45f2d0\" alt=\"w minus 5\"></span></span></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}}