{"id":"cb_question_bank:541e3a68-9dd6-4c37-9aba-c388909678c7","source_id":"cb_question_bank","source_item_id":"541e3a68-9dd6-4c37-9aba-c388909678c7","external_id":"c99660ad-c63a-459b-a649-55773967d912","ibn":null,"question_id":"fe1ec415","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":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A cherry pitting machine pits <math alttext=\"12\"><mn>12</mn>\n</math> pounds of cherries in <math alttext=\"3\"><mn>3</mn>\n</math> minutes. At this rate, how many minutes does it take the machine to pit <math alttext=\"96\"><mn>96</mn>\n</math> pounds of cherries?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It's given that the cherry pitting machine pits <math alttext=\"12\"><mn>12</mn>\n</math> pounds of cherries in <math alttext=\"3\"><mn>3</mn>\n</math> minutes. This rate can be written as&nbsp;<math alttext=\"StartFraction 12 pounds of cherries Over 3 minutes EndFraction\"><mfrac><mrow><mn>12</mn><mo>&nbsp;</mo><mtext>pounds</mtext><mo>&nbsp;</mo><mtext>of</mtext><mo>&nbsp;</mo><mtext>cherries</mtext></mrow><mrow><mn>3</mn><mo>&nbsp;</mo><mtext>minutes</mtext></mrow></mfrac></math>. If the number of minutes it takes the machine to pit <math alttext=\"96\"><mn>96</mn>\n</math> pounds of cherries is represented by <math alttext=\"x\"><mi>x</mi>\n</math>, the value of <math alttext=\"x\"><mi>x</mi>\n</math> can be calculated by solving the equation <math alttext=\"StartFraction 12 pounds of cherries Over 3 minutes EndFraction equals StartFraction 96 pounds of cherries Over x minutes EndFraction\"><mfrac><mrow><mn>12</mn><mo>&nbsp;</mo><mtext>pounds</mtext><mo>&nbsp;</mo><mtext>of</mtext><mo>&nbsp;</mo><mtext>cherries</mtext></mrow><mrow><mn>3</mn><mo>&nbsp;</mo><mtext>minutes</mtext></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>96</mn><mo>&nbsp;</mo><mtext>pounds</mtext><mo>&nbsp;</mo><mtext>of</mtext><mo>&nbsp;</mo><mtext>cherries</mtext></mrow><mrow><mi>x</mi><mo>&nbsp;</mo><mtext>minutes</mtext></mrow></mfrac></math>, which can be rewritten as&nbsp;<math alttext=\"StartFraction 12 Over 3 EndFraction equals StartFraction 96 Over x EndFraction\"><mfrac><mn>12</mn><mn>3</mn></mfrac><mo>=</mo><mfrac><mn>96</mn><mi>x</mi></mfrac></math>, or <math alttext=\"4 equals StartFraction 96 Over x EndFraction\"><mn>4</mn><mo>=</mo><mfrac><mn>96</mn><mi>x</mi></mfrac></math>. Multiplying each side of this equation by <math alttext=\"x\"><mi>x</mi>\n</math> yields&nbsp;<math alttext=\"4 x equals 96\"><mn>4</mn><mi>x</mi><mo>=</mo><mn>96</mn></math>. Dividing each side of this equation by <math alttext=\"4\"><mn>4</mn>\n</math> yields <math alttext=\"x equals 24\"><mi>x</mi><mo>=</mo><mn>24</mn></math>. Therefore, it takes the machine <math alttext=\"24\"><mn>24</mn>\n</math> minutes to pit <math alttext=\"96\"><mn>96</mn>\n</math> pounds of cherries.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the number of minutes it takes the machine to pit <math alttext=\"32\"><mn>32</mn>\n</math>, not <math alttext=\"96\"><mn>96</mn>\n</math>, pounds of cherries.&nbsp;</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the number of minutes it takes the machine to pit <math alttext=\"60\"><mn>60</mn>\n</math>, not <math alttext=\"96\"><mn>96</mn>\n</math>, pounds of cherries.&nbsp;</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the number of minutes it takes the machine to pit <math alttext=\"144\"><mn>144</mn>\n</math>, not <math alttext=\"96\"><mn>96</mn>\n</math>, pounds of cherries.&nbsp;</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.829000+00:00","source_updated_at":"2023-08-02T20:25:59.829000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"8\"><mn>8</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"15\"><mn>15</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"24\"><mn>24</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"36\"><mn>36</mn>\n</math></p>","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}}