{"id":"cb_question_bank:d16a6605-01a5-4859-b68c-f70cb3bc9034","source_id":"cb_question_bank","source_item_id":"d16a6605-01a5-4859-b68c-f70cb3bc9034","external_id":null,"ibn":"070899-DC","question_id":"a04050d8","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The figure presents a 3-column table, with 3 rows of data, titled “Energy per Gram of Typical Macronutrients.” The heading for column 1 is “Macronutrient,” the heading for column 2 is “Food calories,” and the heading for column 3 is “Kilojoules.” The 3 rows of data are as follows. Row 1.Macronutrient, Protein; Food calories, 4 point zero; Kilojoules, 16 point 7. Row 2. Macronutrient, Fat; Food calories, 9 point zero; Kilojoules, 37 point 7. Row 3. Macronutrient, Carbohydrate; Food calories, 4 point zero; Kilojoules, 16 point 7. The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?","stimulus":"","stimulus_html":null,"stem_html":"<p><img src=\"/api/assets/68b177eaef9d5f59abf54b4537e781ba458dc305c7d202a8cd30ae8b79291001\" alt=\"The figure presents a 3-column table, with 3 rows of data, titled “Energy per Gram of Typical Macronutrients.” The heading for column 1 is “Macronutrient,” the heading for column 2 is “Food calories,” and the heading for column 3 is “Kilojoules.” The 3 rows of data are as follows. Row 1.Macronutrient, Protein; Food calories, 4 point zero; Kilojoules, 16 point 7. Row 2. Macronutrient, Fat; Food calories, 9 point zero; Kilojoules, 37 point 7. Row 3. Macronutrient, Carbohydrate; Food calories, 4 point zero; Kilojoules, 16 point 7.\" width=\"191\" height=\"103\"></p><p class=\"stem_paragraph \">The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from <span class=\"italic\">p</span>&nbsp;grams of protein, <span class=\"italic\">f</span>&nbsp;grams of fat, and <span class=\"italic\">c</span>&nbsp;grams of carbohydrate, which of the following expresses <span class=\"italic\">f</span> in terms of <span class=\"italic\">p</span> and <span class=\"italic\">c</span> ?</p><p></p>\n","rationale_html":"<p>Choice B is correct. It is given that there are 4.0 food calories per gram of protein, 9.0 food calories per gram of fat, and 4.0 food calories per gram of carbohydrate. If 180 food calories in a granola bar came from <span class=\"italic\">p</span> grams of protein, <span class=\"italic\">f</span> grams of fat, and <span class=\"italic\">c</span> grams of carbohydrate, then the situation can be represented by the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/22c8f74befe5a200cb49cdf2909aa71147dfb22f2c5e54c5836a8c49d6622098\" alt=\"180 equals, 4 p plus 9 f, plus 4 c\"></span>. The equation can then be rewritten in terms of <span class=\"italic\">f </span>by subtracting 4<span class=\"italic\">p</span> and 4<span class=\"italic\">c </span>from both sides of the equation and then dividing both sides of the equation by 9. The result is the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee099ee304fc9be9802e66640a2b4012405ad8b2b67d9a99cf2ea68974705acb\" alt=\"f equals, 20 minus, four ninths times, open parenthesis, p plus c, close parenthesis\"></span>.</p><p>Choices A, C, and D are incorrect and may be the result of not representing the situation with the correct equation or incorrectly rewriting the equation in terms of <span class=\"italic\">f</span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"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 \">\n              <span class=\"math_expression \">\n                <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ae42233e36ff2c889bf58f53856c37c84dab7a819edb89f4df4e2c96dc2539c\" alt=\"f equals, 20 plus the fraction 4 over 9, end fraction, times, open parenthesis, p plus c, close parenthesis\"></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/ee099ee304fc9be9802e66640a2b4012405ad8b2b67d9a99cf2ea68974705acb\" alt=\"f equals, 20 minus the fraction 4 over 9, end fraction, times, open parenthesis, p plus c, close parenthesis\"></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/0e5a1e1e27d1201790a9cf38596e42bebc74fa462881c00681bb63639c7e3b38\" alt=\"f equals, 20 minus the fraction 4 over 9, end fraction, times, open parenthesis, p minus c, close parenthesis\"></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/d7304d6acd7e67958ef215d1ddd87bd9c6a7bf0f5bcfdabd2c6a80716328c6e0\" alt=\"f equals, 20 plus the fraction 9 over 4, end fraction, times, open parenthesis, p plus c, close parenthesis\"></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}}