{"id":"cb_question_bank:a1fc4b69-8637-42c2-af1f-fc92fafddfb8","source_id":"cb_question_bank","source_item_id":"a1fc4b69-8637-42c2-af1f-fc92fafddfb8","external_id":null,"ibn":"070901-DC","question_id":"520e6f5b","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft 3 ), and the cost per pound, in dollars. The equation 0 point 0 3 times, open parenthesis, 120 w, close parenthesis, plus, 0 point 1 8 times, open parenthesis, 180 z, close parenthesis, plus 3,385 point 8 0, equals 7,576 point 2 0. gives the total cost, in dollars, of the rocks used in the project in terms of the number of ft 3 of limestone, w , and the number of ft 3 of basalt, z . All four rock types are used in the project. Which of the following is the best interpretation of 3,385.80 in this context?","stimulus":"Characteristics for Rock Types Rock type Weight per volume (lb/ft 3 ) Cost per pound Basalt 180 $0.18 Granite 165 $0.09 Limestone 120 $0.03 Sandstone 135 $0.22","stimulus_html":"<div id=\"level-access-access-assistant-highlight-container\">&nbsp;</div><table border=\"1\" cellpadding=\"1\" cellspacing=\"1\" style=\"width: 50%;\"><caption>Characteristics for Rock Types</caption><thead><tr><th scope=\"col\" style=\"text-align: center;\">Rock type</th><th scope=\"col\" style=\"text-align: center;\">Weight per volume (lb/ft<sup>3</sup>)</th><th scope=\"col\" style=\"text-align: center;\">Cost per pound</th></tr></thead><tbody><tr><th scope=\"row\">Basalt</th><td style=\"text-align: center;\">180</td><td style=\"text-align: center;\">$0.18</td></tr><tr><th scope=\"row\">Granite</th><td style=\"text-align: center;\">165</td><td style=\"text-align: center;\">$0.09</td></tr><tr><th scope=\"row\">Limestone</th><td style=\"text-align: center;\">120</td><td style=\"text-align: center;\">$0.03</td></tr><tr><th scope=\"row\">Sandstone</th><td style=\"text-align: center;\">135</td><td style=\"text-align: center;\">$0.22</td></tr></tbody></table>\n","stem_html":"<p class=\"stem_paragraph \">A city is planning to build a rock retaining wall, a monument, and a garden in a park. The table above shows four rock types that will be considered for use in the project. Also shown for each rock type is its weight per volume, in pounds per cubic foot (lb/ft<sup>3</sup>), and the cost per pound, in dollars. The equation <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/83f8cc9799ca1fe941509524d200df524215d12c5044f9edc1a491d945715185\" alt=\"0 point 0 3 times, open parenthesis, 120 w, close parenthesis, plus, 0 point 1 8 times, open parenthesis, 180 z, close parenthesis, plus 3,385 point 8 0, equals 7,576 point 2 0.\"></span></span> gives the total cost, in dollars, of the rocks used in the project in terms of the number of ft<sup>3 </sup>of limestone, <span class=\"italic\">w</span>, and the number of ft<sup>3</sup> of basalt, <span class=\"italic\">z</span>. All four rock types are used in the project. Which of the following is the best interpretation of 3,385.80 in this context?</p>\n","rationale_html":"<p>Choice A is correct. The table shows the cost of limestone is $0.03/lb, and the weight per volume for limestone is 120 lb/ft<sup>3</sup>. Therefore, the term <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/405e2d8301073a49133c8b95bdd84b5e3c9fe6ae31f64dd4d482ebe099dd09ba\" alt=\"0 point 0 3 times 120 w \"></span> represents the cost, in dollars, of <span class=\"italic\">w</span> ft<sup>3</sup> of limestone. Similarly, the term <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/71dc1de413817104a7e7364f1a4696ea4adccea1566d5febc10283ddc7f7afaf\" alt=\"0 point 1 8 times 180 z \"></span> represents the cost, in dollars, of <span class=\"italic\">z</span> ft<sup>3</sup> of basalt. The given equation shows that the total cost of all the rocks used in the project is $7,576.20. Since it’s given that all four rock types are used in the project, the remaining term, 3,385.80, represents the cost, in dollars, of the granite and sandstone needed for the project.</p><p>Choice B is incorrect. The cost of basalt and limestone needed for the project can be represented by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/16e684a021c5db4f3f3c6f5d3493859f1885b890db6725b73b2e03e273bff268\" alt=\"0 point 1 8 times 180 z, plus, 0 point 0 3 times 120 w\"></span>. Choice C is incorrect. The cost of the basalt needed for the project can be represented by the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/71dc1de413817104a7e7364f1a4696ea4adccea1566d5febc10283ddc7f7afaf\" alt=\"0 point 1 8 times 180 z\"></span>. Choice D is incorrect and may result from neglecting to include granite in the rock types used for the project.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.632000+00:00","source_updated_at":"2023-08-02T20:25:59.632000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">The cost of the granite and sandstone needed for the project</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">The cost of the basalt and limestone needed for the project</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">The cost of the basalt needed for the project</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">The cost of the sandstone needed for the project</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}}