{"id":"cb_question_bank:dee8a652-9a37-4137-ac15-c33e7d99ff08","source_id":"cb_question_bank","source_item_id":"dee8a652-9a37-4137-ac15-c33e7d99ff08","external_id":"7375a642-6151-451c-8a97-8c5092f8e9b5","ibn":null,"question_id":"174885f8","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.C.","skill":"Linear equations in two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Jay walks at a speed of 3 miles per hour and runs at a speed of 5 miles per hour. He walks for w hours and runs for r hours for a combined total of 14 miles. Which equation represents this situation?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Jay walks at a speed of <math alttext=\"3\"><mn>3</mn>\n</math> miles per hour and runs at a speed of <math alttext=\"5\"><mn>5</mn>\n</math> miles per hour. He walks for <math alttext=\"w\"><mi>w</mi>\n</math> hours and runs for <math alttext=\"r\"><mi>r</mi>\n</math> hours for a combined total of <math alttext=\"14\"><mn>14</mn>\n</math> miles. Which equation represents this situation?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. Since Jay walks at a speed of <math alttext=\"3\"><mn>3</mn>\n</math> miles per hour for <math alttext=\"w\"><mi>w</mi>\n</math> hours, Jay walks a total of <math alttext=\"3 w\"><mrow>\n\t<mn>3</mn>\n\t<mi>w</mi>\n</mrow>\n</math> miles. Since Jay runs at a speed of <math alttext=\"5\"><mn>5</mn>\n</math> miles per hour for <math alttext=\"r\"><mi>r</mi>\n</math> hours, Jay runs a total of <math alttext=\"5 r\"><mrow>\n\t<mn>5</mn>\n\t<mi>r</mi>\n</mrow>\n</math> miles. Therefore, the total number of miles Jay travels can be represented by <math alttext=\"3 w plus 5 r\"><mn>3</mn><mi>w</mi><mo>+</mo><mn>5</mn><mi>r</mi></math>. Since the combined total number of miles is <math alttext=\"14\"><mn>14</mn>\n</math>, the equation <math alttext=\"3 w plus 5 r equals 14\"><mn>3</mn><mi>w</mi><mo>+</mo><mn>5</mn><mi>r</mi><mo>=</mo><mn>14</mn></math> represents this situation.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.813000+00:00","source_updated_at":"2023-08-02T20:25:59.813000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"3 w plus 5 r equals 14\"><mn>3</mn><mi>w</mi><mo>+</mo><mn>5</mn><mi>r</mi><mo>=</mo><mn>14</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"one third w plus one fifth r equals 14\"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>w</mi><mo>+</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>r</mi><mo>=</mo><mn>14</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"one third w plus one fifth r equals 112\"><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>w</mi><mo>+</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mi>r</mi><mo>=</mo><mn>112</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"3 w plus 5 r equals 112\"><mn>3</mn><mi>w</mi><mo>+</mo><mn>5</mn><mi>r</mi><mo>=</mo><mn>112</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}}