{"id":"cb_question_bank:defff91a-c49c-4717-b6b0-6ed31c3baef7","source_id":"cb_question_bank","source_item_id":"defff91a-c49c-4717-b6b0-6ed31c3baef7","external_id":"0f9a48e3-fac3-492a-8104-05def2d974ce","ibn":null,"question_id":"441558e7","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Scientists collected fallen acorns that each housed a colony of the ant species P. ohioensis and analyzed each colony's structure. For any of these colonies, if the colony has x worker ants, the equation y equals 0.67 x plus 2.6 , where 20 less than or equals x less than or equals 110 , gives the predicted number of larvae, y , in the colony. If one of these colonies has 58 worker ants, which of the following is closest to the predicted number of larvae in the colony?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Scientists collected fallen acorns that each housed a colony of the ant species <em>P. ohioensis</em>&nbsp;and analyzed each colony's structure. For any of these colonies, if the colony has <math alttext=\"x\"><mi>x</mi>\n</math> worker ants, the equation&nbsp;<math alttext=\"y equals 0.67 x plus 2.6\"><mi>y</mi><mo>=</mo><mn>0.67</mn><mi>x</mi><mo>+</mo><mn>2.6</mn></math>, where&nbsp;<math alttext=\"20 less than or equals x less than or equals 110\"><mn>20</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>110</mn></math>, gives the predicted number of larvae, <math alttext=\"y\"><mi>y</mi>\n</math>, in the colony. If one of these colonies has <math alttext=\"58\"><mn>58</mn>\n</math> worker ants, which of the following is closest to the predicted number of larvae in the colony?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that the equation&nbsp;<math alttext=\"y equals 0.67 x plus 2.6\"><mi>y</mi><mo>=</mo><mn>0.67</mn><mi>x</mi><mo>+</mo><mn>2.6</mn></math>, where&nbsp;<math alttext=\"20 less than or equals x less than or equals 110\"><mn>20</mn><mo>≤</mo><mi>x</mi><mo>≤</mo><mn>110</mn></math>, gives the predicted number of larvae, <math alttext=\"y\"><mi>y</mi>\n</math>, in a colony of ants if the colony has <math alttext=\"x\"><mi>x</mi>\n</math> worker ants. If one of these colonies has <math alttext=\"58\"><mn>58</mn>\n</math> worker ants, the predicted number of larvae in that colony can be found by substituting <math alttext=\"58\"><mn>58</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation. Substituting <math alttext=\"58\"><mn>58</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the given equation yields <math alttext=\"y equals 0.67 left parenthesis 58 right parenthesis plus 2.6\"><mi>y</mi><mo>=</mo><mn>0.67</mn><mfenced><mn>58</mn></mfenced><mo>+</mo><mn>2.6</mn></math>, or <math alttext=\"y equals 41.46\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>41.46</mn>\n</mrow>\n</math>. Of the given choices, <math alttext=\"41\"><mn>41</mn>\n</math> is closest to the predicted number of larvae in the colony.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is closest to the predicted number of larvae in a colony with <math alttext=\"87\"><mn>87</mn>\n</math> worker ants.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is closest to the number of worker ants for which the predicted number of larvae in a colony is <math alttext=\"58\"><mn>58</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is closest to the predicted number of larvae in a colony with <math alttext=\"280\"><mn>280</mn>\n</math> worker ants.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.812000+00:00","source_updated_at":"2023-08-02T20:25:59.812000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"41\"><mn>41</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"61\"><mn>61</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"83\"><mn>83</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"190\"><mn>190</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}}