{"id":"cb_question_bank:ed33d33d-606e-4fe5-96d7-2d069ac3ea05","source_id":"cb_question_bank","source_item_id":"ed33d33d-606e-4fe5-96d7-2d069ac3ea05","external_id":"56ef2f00-3bce-4eb9-bc8b-077ee70a054d","ibn":null,"question_id":"12ae3452","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation 46 equals 2 a plus 2 b gives the relationship between the side lengths a and b of a certain parallelogram. If a equals 9 , what is the value of b ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">The equation <math alttext=\"46 equals 2 a plus 2 b\"><mrow>\n\t<mn>46</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>a</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>b</mi>\n\t\t</mrow>\n\t</mrow>\n</mrow>\n</math> gives the relationship between the side lengths <math alttext=\"a\"><mi>a</mi>\n</math> and <math alttext=\"b\"><mi>b</mi>\n</math> of a certain parallelogram. If <math alttext=\"a equals 9\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mn>9</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"b\"><mi>b</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"14\"><mn>14</mn>\n</math>. It's given that the equation&nbsp;<math alttext=\"46 equals 2 a plus 2 b\"><mn>46</mn><mo>=</mo><mn>2</mn><mi>a</mi><mo>+</mo><mn>2</mn><mi>b</mi></math> gives the relationship between the side lengths <math alttext=\"a\"><mi>a</mi>\n</math> and <math alttext=\"b\"><mi>b</mi>\n</math> of a certain parallelogram. Substituting <math alttext=\"9\"><mn>9</mn>\n</math> for <math alttext=\"a\"><mi>a</mi>\n</math> in the given equation&nbsp;yields <math alttext=\"46 equals 2 left parenthesis 9 right parenthesis plus 2 b\"><mn>46</mn><mo>=</mo><mn>2</mn><mfenced><mn>9</mn></mfenced><mo>+</mo><mn>2</mn><mi>b</mi></math>, or <math alttext=\"46 equals 18 plus 2 b\"><mn>46</mn><mo>=</mo><mn>18</mn><mo>+</mo><mn>2</mn><mi>b</mi></math>. Subtracting <math alttext=\"18\"><mn>18</mn>\n</math> from both sides of this equation yields <math alttext=\"28 equals 2 b\"><mn>28</mn><mo>=</mo><mn>2</mn><mi>b</mi></math>. Dividing both sides of this equation by <math alttext=\"2\"><mn>2</mn>\n</math> yields <math alttext=\"14 equals b\"><mn>14</mn><mo>=</mo><mi>b</mi></math>. Therefore, if <math alttext=\"a equals 9\"><mi>a</mi><mo>=</mo><mn>9</mn></math>, the value of <math alttext=\"b\"><mi>b</mi>\n</math> is <math alttext=\"14\"><mn>14</mn>\n</math>.</p>","correct_answer":["14"],"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":[],"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}}