{"id":"cb_question_bank:c750517a-f0ef-4435-b4da-d8c2a0974000","source_id":"cb_question_bank","source_item_id":"c750517a-f0ef-4435-b4da-d8c2a0974000","external_id":"eb660cfe-6d9e-465b-a9a3-9b5a5ae60195","ibn":null,"question_id":"637022d2","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"2.5 b plus 5 r equals 80 The given equation describes the relationship between the number of birds, b , and the number of reptiles, r , that can be cared for at a pet care business on a given day. If the business cares for 16 reptiles on a given day, how many birds can it care for on this day?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"2.5 b plus 5 r equals 80\"><mn>2.5</mn><mi>b</mi><mo>+</mo><mn>5</mn><mi>r</mi><mo>=</mo><mn>80</mn></math></p>\n<p style=\"text-align: left;\">The given equation describes the relationship between the number of birds, <math alttext=\"b\"><mi>b</mi>\n</math>, and the number of reptiles, <math alttext=\"r\"><mi>r</mi>\n</math>, that can be cared for at a pet care business on a given day. If the business cares for <math alttext=\"16\"><mn>16</mn>\n</math> reptiles on a given day, how many birds can it care for on this day?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The number of birds can be found by calculating the value of <math alttext=\"b\"><mi>b</mi>\n</math> when <math alttext=\"r equals 16\"><mrow>\n\t<mi>r</mi>\n\t<mo>=</mo>\n\t<mn>16</mn>\n</mrow>\n</math> in the given equation. Substituting <math alttext=\"16\"><mn>16</mn>\n</math> for <math alttext=\"r\"><mi>r</mi>\n</math> in the given equation yields <math alttext=\"2.5 b plus 5 left parenthesis 16 right parenthesis equals 80\"><mn>2.5</mn><mi>b</mi><mo>+</mo><mn>5</mn><mfenced><mn>16</mn></mfenced><mo>=</mo><mn>80</mn></math>, or <math alttext=\"2.5 b plus 80 equals 80\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>2.5</mn>\n\t\t\t<mi>b</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>80</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>80</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"80\"><mn>80</mn>\n</math> from both sides of this equation yields <math alttext=\"2.5 b equals 0\"><mrow>\n\t<mrow>\n\t\t<mn>2.5</mn>\n\t\t<mi>b</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"2.5\"><mn>2.5</mn>\n</math> yields <math alttext=\"b equals 0\"><mrow>\n\t<mi>b</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Therefore, if the business cares for <math alttext=\"16\"><mn>16</mn>\n</math> reptiles on a given day, it can care for <math alttext=\"0\"><mn>0</mn>\n</math> birds on this day.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.815000+00:00","source_updated_at":"2023-08-02T20:25:59.815000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"0\"><mn>0</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"40\"><mn>40</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"80\"><mn>80</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}}