{"id":"cb_question_bank:81f35cb9-5a4b-4042-9980-32aa8af3e40b","source_id":"cb_question_bank","source_item_id":"81f35cb9-5a4b-4042-9980-32aa8af3e40b","external_id":"700cd854-082d-4c3c-a2da-017482d48062","ibn":null,"question_id":"a309803e","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of w square feet. Which equation represents the total amount of paint upper P , in gallons, needed to paint the walls of the room twice?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">One gallon of paint will cover <math alttext=\"220\"><mn>220</mn>\n</math> square feet of a surface. A room has a total wall area of <math alttext=\"w\"><mi>w</mi>\n</math><em>&nbsp;</em>square feet. Which equation represents the total amount of paint <math alttext=\"upper P\"><mi>P</mi>\n</math>, in gallons, needed to paint the walls of the room twice?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. It's given that <math alttext=\"w\"><mi>w</mi>\n</math> represents the total wall area, in square feet. Since the walls of the room will be painted twice, the amount of paint, in gallons, needs to cover <math alttext=\"2 w\"><mrow>\n\t<mn>2</mn>\n\t<mi>w</mi>\n</mrow>\n</math> square feet. It’s also given that one gallon of paint will cover <math alttext=\"220\"><mn>220</mn>\n</math> square feet. Dividing the total area, in square feet, of the surface to be painted by the number of square feet covered by one gallon of paint gives the number of gallons of paint that will be needed. Dividing <math alttext=\"2 w\"><mrow>\n\t<mn>2</mn>\n\t<mi>w</mi>\n</mrow>\n</math> by <math alttext=\"220\"><mn>220</mn>\n</math> yields &nbsp;<math alttext=\"StartFraction 2 w Over 220 EndFraction\"><mfrac><mrow><mn>2</mn><mi>w</mi></mrow><mn>220</mn></mfrac></math>, or <math alttext=\"StartFraction w Over 110 EndFraction\"><mfrac><mi>w</mi><mn>110</mn></mfrac></math>. Therefore, the equation that represents the total amount of paint <math alttext=\"upper P\"><mi>P</mi>\n</math>, in gallons, needed to paint the walls of the room twice is <math alttext=\"upper P equals StartFraction w Over 110 EndFraction\"><mi>P</mi><mo>=</mo><mfrac><mi>w</mi><mn>110</mn></mfrac></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from finding the amount of paint needed to paint the walls once rather than twice.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.810000+00:00","source_updated_at":"2023-08-02T20:25:59.810000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"upper P equals StartFraction w Over 110 EndFraction\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>w</mi>\n\t\t\t<mn>110</mn>\n\t\t</mfrac>\n\t</mrow>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"upper P equals 440 w\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>440</mn>\n\t\t<mi>w</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"upper P equals StartFraction w Over 220 EndFraction\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mfrac>\n\t\t\t<mi>w</mi>\n\t\t\t<mn>220</mn>\n\t\t</mfrac>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"upper P equals 220 w\"><mrow>\n\t<mi>P</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>220</mn>\n\t\t<mi>w</mi>\n\t</mrow>\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}}