{"id":"cb_question_bank:842ea340-7c9a-40d2-b26d-30a08dfc448c","source_id":"cb_question_bank","source_item_id":"842ea340-7c9a-40d2-b26d-30a08dfc448c","external_id":"c19a1158-3fde-4af0-be5d-79e3722ddf7e","ibn":null,"question_id":"5b2b8866","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A rectangular poster has an area of 360 square inches. A copy of the poster is made in which the length and width of the original poster are each increased by 20 percent sign . What is the area of the copy, in square inches?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A rectangular poster has an area of <math alttext=\"360\"><mn>360</mn>\n</math> square inches. A copy of the poster is made in which the length and width of the original poster are each increased by <math alttext=\"20 percent sign\"><mn>20</mn>\n<mo>%</mo></math>. What is the area of the copy, in square inches?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"518.4\"><mn>518.4</mn>\n</math>. It's given that the area of the original poster is <math alttext=\"360\"><mn>360</mn>\n</math> square inches. Let&nbsp;<math alttext=\"script l\"><mi>l</mi></math> represent the length, in inches, of the original poster, and let <math alttext=\"w\"><mi>w</mi>\n</math> represent the width, in inches, of the original poster. Since the area of a rectangle is equal to its length times its width, it follows that <math alttext=\"360 equals script l w\"><mn>360</mn><mo>=</mo><mi>l</mi><mi>w</mi></math>. It's also given that a copy of the poster is made in which the length and width of the original poster are each increased by <math alttext=\"20 percent sign\"><mn>20</mn><mo>%</mo></math>. It follows that the length of the copy is the length of the original poster plus&nbsp;<math alttext=\"20 percent sign\"><mn>20</mn><mo>%</mo></math> of the length of the original poster, which is equivalent to&nbsp;<math alttext=\"script l plus StartFraction 20 Over 100 EndFraction script l\"><mi>l</mi><mo>+</mo><mfrac><mn>20</mn><mn>100</mn></mfrac><mi>l</mi></math> inches. This length can be rewritten as <math alttext=\"script l plus 0.2 script l\"><mi>l</mi><mo>+</mo><mn>0.2</mn><mi>l</mi></math> inches, or&nbsp;<math alttext=\"1.2 script l\"><mn>1.2</mn><mi>l</mi></math> inches. Similarly, the width of the copy is the width of the original poster plus&nbsp;<math alttext=\"20 percent sign\"><mn>20</mn><mo>%</mo></math> of the width of the original poster, which is equivalent to&nbsp;<math alttext=\"w plus StartFraction 20 Over 100 EndFraction w\"><mi>w</mi><mo>+</mo><mfrac><mn>20</mn><mn>100</mn></mfrac><mi>w</mi></math> inches. This width can be rewritten as&nbsp;<math alttext=\"w plus 0.2 w\"><mi>w</mi><mo>+</mo><mn>0.2</mn><mi>w</mi></math> inches, or <math alttext=\"1.2 w\"><mn>1.2</mn><mi>w</mi></math> inches. Since the area of a rectangle is equal to its length times its width, it follows that the area, in square inches, of the copy is equal to&nbsp;<math alttext=\"left parenthesis 1.2 script l right parenthesis left parenthesis 1.2 w right parenthesis\"><mfenced><mrow><mn>1.2</mn><mi>l</mi></mrow></mfenced><mfenced><mrow><mn>1.2</mn><mi>w</mi></mrow></mfenced></math>, which can be rewritten as <math alttext=\"left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis script l w right parenthesis\"><mfenced><mn>1.2</mn></mfenced><mfenced><mn>1.2</mn></mfenced><mfenced><mrow><mi>l</mi><mi>w</mi></mrow></mfenced></math>. Since <math alttext=\"360 equals script l w\"><mn>360</mn><mo>=</mo><mi>l</mi><mi>w</mi></math>, the area, in square inches, of the copy can be found by substituting <math alttext=\"360\"><mn>360</mn>\n</math> for&nbsp;<math alttext=\"script l w\"><mi>l</mi><mi>w</mi></math> in the expression&nbsp;<math alttext=\"left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis script l w right parenthesis\"><mfenced><mn>1.2</mn></mfenced><mfenced><mn>1.2</mn></mfenced><mfenced><mrow><mi>l</mi><mi>w</mi></mrow></mfenced></math>, which yields <math alttext=\"left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis 360 right parenthesis\"><mfenced><mn>1.2</mn></mfenced><mfenced><mn>1.2</mn></mfenced><mfenced><mn>360</mn></mfenced></math>, or <math alttext=\"518.4\"><mn>518.4</mn>\n</math>. Therefore, the area of the copy, in square inches, is <math alttext=\"518.4\"><mn>518.4</mn>\n</math>.</p>","correct_answer":["2592/5","518.4"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.837000+00:00","source_updated_at":"2023-08-02T20:25:59.837000+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}}