{"id":"cb_question_bank:b46c091e-5dd7-4a5c-a2e6-0a9a2c2c7345","source_id":"cb_question_bank","source_item_id":"b46c091e-5dd7-4a5c-a2e6-0a9a2c2c7345","external_id":"a1a5d2fd-4a30-4105-b4de-ee544853263c","ibn":null,"question_id":"551c52b9","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Tilly earns p dollars for every w hours of work. Which expression represents the amount of money, in dollars, Tilly earns for 39 w hours of work?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Tilly earns <math alttext=\"p\"><mi>p</mi>\n</math> dollars for every <math alttext=\"w\"><mi>w</mi>\n</math> hours of work. Which expression represents the amount of money, in dollars, Tilly earns for <math alttext=\"39 w\"><mrow>\n\t<mn>39</mn>\n\t<mi>w</mi>\n</mrow>\n</math> hours of work?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It’s given that Tilly earns <math alttext=\"p\"><mi>p</mi>\n</math> dollars for every <math alttext=\"w\"><mi>w</mi>\n</math> hours of work. This can be represented by the proportion <math alttext=\"StartFraction p Over w EndFraction\"><mfrac><mi>p</mi><mi>w</mi></mfrac></math>. The amount of money, <math alttext=\"x\"><mi>x</mi>\n</math>, Tilly earns for <math alttext=\"39 w\"><mrow>\n\t<mn>39</mn>\n\t<mi>w</mi>\n</mrow>\n</math> hours of work can be found by setting up the proportion <math alttext=\"StartFraction p Over w EndFraction equals StartFraction x Over 39 w EndFraction\"><mfrac><mi>p</mi><mi>w</mi></mfrac><mo>=</mo><mfrac><mi>x</mi><mrow><mn>39</mn><mi>w</mi></mrow></mfrac></math>. This can be rewritten as <math alttext=\"39 p w equals x w\"><mn>39</mn><mi>p</mi><mi>w</mi><mo>=</mo><mi>x</mi><mi>w</mi></math>. Dividing both sides by <math alttext=\"w\"><mi>w</mi>\n</math> results in <math alttext=\"x equals 39 p\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>39</mn>\n\t\t<mi>p</mi>\n\t</mrow>\n</mrow>\n</math>.&nbsp;</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the amount of money Tilly earns in dollars per hour, not the amount of money Tilly earns for <math alttext=\"39 w\"><mrow>\n\t<mn>39</mn>\n\t<mi>w</mi>\n</mrow>\n</math> hours of work.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the amount of money Tilly earns for <math alttext=\"w\"><mi>w</mi>\n</math> hours of work plus <math alttext=\"39\"><mn>39</mn>\n</math>, not the amount of money Tilly earns for <math alttext=\"39 w\"><mrow>\n\t<mn>39</mn>\n\t<mi>w</mi>\n</mrow>\n</math> hours of work.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is the amount of money Tilly earns for <math alttext=\"w\"><mi>w</mi>\n</math> hours of work minus <math alttext=\"39\"><mn>39</mn>\n</math>, not the amount of money Tilly earns for <math alttext=\"39 w\"><mrow>\n\t<mn>39</mn>\n\t<mi>w</mi>\n</mrow>\n</math> hours of work.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.830000+00:00","source_updated_at":"2023-08-02T20:25:59.830000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"39 p\"><mrow>\n\t<mn>39</mn>\n\t<mi>p</mi>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"StartFraction p Over 39 EndFraction\"><mfrac><mi>p</mi><mn>39</mn></mfrac></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"p plus 39\"><mrow>\n\t<mi>p</mi>\n\t<mo>+</mo>\n\t<mn>39</mn>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"p minus 39\"><mrow>\n\t<mi>p</mi>\n\t<mo>-</mo>\n\t<mn>39</mn>\n</mrow>\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}}