{"id":"cb_question_bank:99d036e7-f00d-44b9-9f34-c1c9f6b6c15d","source_id":"cb_question_bank","source_item_id":"99d036e7-f00d-44b9-9f34-c1c9f6b6c15d","external_id":null,"ibn":"021851-DC","question_id":"431c3038","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In an article about exercise, it is estimated that a 160-pound adult uses 200 calories for every 30 minutes of hiking and 150 calories for every 30 minutes of bicycling. An adult who weighs 160 pounds has completed 1 hour of bicycling. Based on the article, how many hours should the adult hike to use a total of 1,900 calories from bicycling and hiking?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In an article about exercise, it is estimated that a&nbsp;160-pound adult uses 200 calories for every 30&nbsp;minutes of hiking and 150 calories for every 30&nbsp;minutes of bicycling. An adult who weighs 160&nbsp;pounds has completed 1&nbsp;hour of bicycling. Based on the article, how many hours should the adult hike to use a total of 1,900&nbsp;calories from bicycling and hiking?</p>\n","rationale_html":"<p>Choice D is correct. Since a 160-pound adult uses 200 calories for every 30 minutes of hiking, then the same adult uses <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f12cf0c0a088c9e8a2b82f3a5723c1cc16537256b19d007cd3da11320a2a5fca\" alt=\"200 h\"></span> calories after hiking for <span class=\"italic\">h</span> 30-minute periods. Similarly, the same adult uses <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/20b15e14d7a5fd288d9bc3cab92765abb905ddc92b4ca953c23beef699e72313\" alt=\"150 b\"></span> calories after bicycling for <span class=\"italic\">b</span> 30-minute periods. Therefore, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/084f4f2cd2c76df0787c9c971692bc6308e7e5fd3b2b7a6ff523105dd37a9028\" alt=\"200 h plus 150 b, equals 1,900 \"></span> represents the situation where a 160-pound adult uses a total of 1,900 calories from hiking for <span class=\"italic\">h</span> 30-minute periods and bicycling for <span class=\"italic\">b</span> 30-minute periods. It’s given that the adult completes 1 hour, or 2 30-minute periods, of bicycling. Substituting 2 for <span class=\"italic\">b</span> in the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/084f4f2cd2c76df0787c9c971692bc6308e7e5fd3b2b7a6ff523105dd37a9028\" alt=\"200 h plus 150 b, equals 1,900 \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6130179a3915da11d76f011515fad7bc3b3be54d3a86d6fa2d21c5901eba0ae8\" alt=\"200 h plus, 150 times 2, equals 1,900\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dc063da3c0fb971a26c425dabac41d49e9057ad0b06a473fb2813733d38ca614\" alt=\"200 h plus 300, equals 1,900\"></span>. Subtracting 300 from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e650e130495b619271cab1b968bac4f153afd76bdb1aa0261025902362ccc4cc\" alt=\"200 h equals 1,600\"></span>. Dividing both sides by 200 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c2f972515ae3f10c787fbc4ba2dcb2b0cbb313edb144f8675524cc7f81c5a3b\" alt=\"h equals 8\"></span>. Since <span class=\"italic\">h</span> represents the number of 30-minute periods spent hiking and there are 2 30-minute periods in every hour, it follows that the adult will need to hike for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1cf3ca6125063879a4d297324a1045a2d445d2dcd5284cceeb025bd61d46fb4a\" alt=\"the fraction eight over 2\"></span>, or 4 hours to use a total of 1,900 calories from bicycling and hiking.</p><p>Choice A is incorrect and may result from solving the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6106110eb3a7bf730e258761d3c07688c37c3d0269bc25b152b79d613d60ae46\" alt=\"200 h equals 1,900\"></span>. This represents 0 30-minute periods bicycling instead of 2. Choice B is incorrect and may result from solving the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/13a93c5b731d1ff876ead69942a334dc47784bce2e0e2455454f639e29d37e13\" alt=\"200 h plus 150, equals 1,900\"></span>. This represents 1 30-minute period of bicycling instead of 2. Choice C is incorrect. This may result from determining that the number of 30-minute periods the adult should hike is 8, but then subtracting 2 from 8, rather than dividing 8 by 2, to find the number of <u><span class=\"underline\">hours</span></u> the adult should hike.&nbsp;</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">9.5</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">8.75</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">6</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">4</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}}