{"id":"cb_question_bank:2d6cadce-4a6b-490d-b122-9f54b59140ea","source_id":"cb_question_bank","source_item_id":"2d6cadce-4a6b-490d-b122-9f54b59140ea","external_id":null,"ibn":"09372-DC","question_id":"71189542","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A group of 202&nbsp;people went on an overnight camping trip, taking 60&nbsp;tents with them. Some of the tents held 2&nbsp;people each, and the rest held 4&nbsp;people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?</p>\n","rationale_html":"<p>Choice C is correct. Let <span class=\"italic\">x</span> represent the number of 2-person tents and let <span class=\"italic\">y</span> represent the number of 4-person tents. It is given that the total number of tents was 60 and the total number of people in the group was 202. This situation can be expressed as a system of two equations, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4df1dd27defb72f3f9e096e3c31d8ea6c174991b6949717078e48c0db236e8fa\" alt=\"x plus y, equals 60\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/098b957e17f1691580780ccf26220398129c849430a276c439e54264c1f4954b\" alt=\"2 x plus 4 y, equals 202\"></span>. The first equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aca5bf11883fe10da430a0863aa53389227c650de317f2c6ae381d0d8f4d25ec\" alt=\"y equals, negative x plus 60\"></span>. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc6d1ad657b0e456ec98e8aa367c0c9f50d20765ad33e642aa9303f2c6f762f0\" alt=\"negative x plus 60\"></span> for <span class=\"italic\">y</span> in the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/098b957e17f1691580780ccf26220398129c849430a276c439e54264c1f4954b\" alt=\"2 x plus 4 y, equals 202\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8819d3556b2d22479ad64e17d9849ab2565c79a79eedc46c7fe2734ee70afb9f\" alt=\"2 x plus, 4 times, open parenthesis, negative x plus 60, close parenthesis, equals 202\"></span>. Distributing and combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/66813ed7ced382d7d53dbc867d2648d31c337e3aa385811d54fa8914e7e43099\" alt=\"negative 2 x plus 240, equals 202\"></span>. Subtracting 240 from both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/66813ed7ced382d7d53dbc867d2648d31c337e3aa385811d54fa8914e7e43099\" alt=\"negative 2 x plus 240, equals 202\"></span> and then dividing both sides by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a546b5be2c97283e2d1e93605f422844d5a87f3418a61a7d23019eb596b64f17\" alt=\"negative 2\"></span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/30b5677a948bfc9df515d35a71dec525ca5c9e8c02a2bf0b67a0530849cc2639\" alt=\"x equals 19\"></span>. Therefore, the number of 2-person tents is 19.</p><p>Alternate approach: If each of the 60 tents held 4 people, the total number of people that could be accommodated in tents would be 240. However, the actual number of people who slept in tents was 202. The difference of 38 accounts for the 2-person tents. Since each of these tents holds 2 people fewer than a 4-person tent, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c9dd496c6e3f5a919062ffb506256778a14a81ce0444893fadb36861d0c9a1c2\" alt=\"thirty eight halves, equals 19\"></span> gives the number of 2-person tents.</p><p>Choice A is incorrect. This choice may result from assuming exactly half of the tents hold 2 people. If that were true, then the total number of people who slept in tents would be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ea9eae8ad620f3dcfcbb8f6fd41da560ca3509cbbbac86891dd53334322f4641\" alt=\"2 times 30, plus, 4 times 30, equals 180\"></span>; however, the total number of people who slept in tents was 202, not 180. Choice B is incorrect. If 20 tents were 2-person tents, then the remaining 40 tents would be 4-person tents. Since all the tents were filled to capacity, the total number of people who slept in tents would be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d5906e22923acb76990fd84bc956640e1b64291267f9d5f96a7fd9d1425adcc\" alt=\"2 times 20, plus, 4 times 40, equals, 40 plus 160, which equals 200\"></span>; however, the total number of people who slept in tents was 202, not 200. Choice D is incorrect. If 18 tents were 2-person tents, then the remaining 42 tents would be 4-person tents. Since all the tents were filled to capacity, the total number of people who slept in tents would be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/39f2addc9529b0898c5af4914fc94abcb3dd7a94e1f7888ddf155ac926df3518\" alt=\"2 times 18, plus, 4 times 42, equals, 36 plus 168, which equals 204\"></span>; however, the total number of people who slept in tents was 202, not 204. </p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p>30</p>\n","ord":0},{"label":"B","content_html":"<p>20</p>\n","ord":1},{"label":"C","content_html":"<p>19</p>\n","ord":2},{"label":"D","content_html":"<p>18</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}}