{"id":"cb_question_bank:9ed94d96-4274-403d-a5e1-275e212b8abb","source_id":"cb_question_bank","source_item_id":"9ed94d96-4274-403d-a5e1-275e212b8abb","external_id":null,"ibn":"019519-DC","question_id":"b76a2815","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The power P produced by a machine is represented by the equation above, where W is the work performed during an amount of time t . Which of the following correctly expresses W in terms of P and t ?","stimulus":"P equals, the fraction W over t","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cdcf7f94cd00c47ffae10da722884383cb7d54b28782be40fdfb3f5a080cab59\" alt=\"P equals, the fraction W over t\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The power <span class=\"italic\">P</span> produced by a machine is represented by the equation above, where <span class=\"italic\">W</span> is the work performed during an amount of time <span class=\"italic\">t</span>. Which of the following correctly expresses <span class=\"italic\">W</span> in terms of <span class=\"italic\">P</span> and <span class=\"italic\">t</span> ?</p>\n","rationale_html":"<p>Choice A is correct. Multiplying both sides of the equation by <span class=\"italic\">t </span>yields&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe260cb65283268e47be73eb0e5c544b1c20ed3da4892adb9a87860bd9e1972b\" alt=\"P times t equals, open parenthesis, the fraction w over t, close parenthesis, times t\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0207a793f2f3c94ba3e462c200c78afb26a2d7421b17bf948573a90c263f1e32\" alt=\"P t equals W\"></span>, which expresses <span class=\"italic\">W</span> in terms of <span class=\"italic\">P</span> and <span class=\"italic\">t</span>. This is equivalent to <span class=\"italic\">W</span> = <span class=\"italic\">Pt</span>.</p><p>\n        <br>\nChoices B, C, and D are incorrect. Each of the expressions given in these answer choices gives <span class=\"italic\">W</span> in terms of <span class=\"italic\">P</span> and <span class=\"italic\">t</span>&nbsp;but doesn’t maintain the given relationship between <span class=\"italic\">W</span>,<span class=\"italic\"> P</span>, and <span class=\"italic\">t</span>. These expressions may result from&nbsp;performing different operations with <span class=\"italic\">t</span> on each side of the equation. In choice B, <span class=\"italic\">W</span> has been multiplied by <span class=\"italic\">t</span>, and <span class=\"italic\">P </span>has been divided by <span class=\"italic\">t.</span> In choice C, <span class=\"italic\">W</span> has been multiplied by <span class=\"italic\">t</span>,&nbsp;and the quotient of <span class=\"italic\">P</span> divided by <span class=\"italic\">t </span>has been reciprocated. In choice D, <span class=\"italic\">W</span> has been multiplied by<span class=\"italic\"> t</span>, and<span class=\"italic\"> P</span> has been added to <span class=\"italic\">t</span>. However, in order to maintain the relationship between the variables in the given equation, the same operation must be performed with<span class=\"italic\"> t</span> on each side of the equation.&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/48bc38e2afbfdf6622abb6bf2c92b509b590d300b95e039eb3256ac8fe55c429\" alt=\"W equals, P t\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1ab2a6ba9751b2299a186c069e73bf231bce10a0848c17cdb7ae7be901e426f0\" alt=\"W equals, the fraction P over t\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0cc44a0d5301570571476727ec8ca3115925b133e1a9c02a16b3913531569a7e\" alt=\"W equals, the fraction t over P\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5f56571a827492f3b82d486c4699e833d80765663abad9a6486320f3bdbb7cbb\" alt=\"W equals, P plus t\"></span></span>\n          </p>\n","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}}