{"id":"cb_question_bank:37040fdb-dd9f-4730-ab4b-32d10009beca","source_id":"cb_question_bank","source_item_id":"37040fdb-dd9f-4730-ab4b-32d10009beca","external_id":"67336474-3a8f-4702-9694-98a3abdcc31a","ibn":null,"question_id":"2f0a43b2","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.A.","skill":"Linear equations in one variable","difficulty":"E","score_band":3,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If StartFraction x Over 8 EndFraction equals 5 , what is the value of StartFraction 8 Over x EndFraction ?","stimulus":"","stimulus_html":null,"stem_html":"<p>If <math alttext=\"StartFraction x Over 8 EndFraction equals 5\"><mrow>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>8</mn>\n\t\t</mfrac>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"StartFraction 8 Over x EndFraction\"><mrow>\n\t<mfrac>\n\t\t<mn>8</mn>\n\t\t<mi>x</mi>\n\t</mfrac>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"one fifth\"><mfrac><mn>1</mn><mn>5</mn></mfrac></math>. Since the number <math alttext=\"5\"><mn>5</mn>\n</math> can also be written as <math alttext=\"five oneths\"><mfrac><mn>5</mn><mn>1</mn></mfrac></math>, the given equation can also be written as <math alttext=\"StartFraction x Over 8 EndFraction equals five oneths\"><mfrac><mi>x</mi><mn>8</mn></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>1</mn></mfrac></math>. This equation is equivalent to&nbsp;<math alttext=\"StartFraction 8 Over x EndFraction equals one fifth\"><mfrac><mn>8</mn><mi>x</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></math>. Therefore, the value of <math alttext=\"StartFraction 8 Over x EndFraction\"><mfrac><mn>8</mn><mi>x</mi></mfrac></math> is <math alttext=\"one fifth\"><mfrac><mn>1</mn><mn>5</mn></mfrac></math>. Note that 1/5 and .2 are examples of ways to enter a correct answer.</p>\n<p style=\"text-align: left;\">Alternate approach: Multiplying both sides of the equation <math alttext=\"StartFraction x Over 8 EndFraction equals 5\"><mfrac><mi>x</mi><mn>8</mn></mfrac><mo>=</mo><mn>5</mn></math> by <math alttext=\"8\"><mn>8</mn>\n</math> yields <math alttext=\"x equals 40\"><mi>x</mi><mo>=</mo><mn>40</mn></math>. Substituting <math alttext=\"40\"><mn>40</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> into the expression&nbsp;<math alttext=\"StartFraction 8 Over x EndFraction\"><mfrac><mn>8</mn><mi>x</mi></mfrac></math> yields <math alttext=\"eight fortieths\"><mfrac><mn>8</mn><mn>40</mn></mfrac></math>, or&nbsp;<math alttext=\"one fifth\"><mfrac><mn>1</mn><mn>5</mn></mfrac></math>.&nbsp;</p>","correct_answer":[".2","1/5"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.808000+00:00","source_updated_at":"2023-08-02T20:25:59.808000+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}}