{"id":"cb_question_bank:7f549211-39b5-4567-8933-74ff3b21eb88","source_id":"cb_question_bank","source_item_id":"7f549211-39b5-4567-8933-74ff3b21eb88","external_id":null,"ibn":"028813-DC","question_id":"4fe4fd7c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.B.","skill":"Linear functions","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A company’s total cost c of x , in dollars, to produce x shirts is given by the function above, where m is a constant and x is greater than 0 . The total cost to produce 100 shirts is $800. What is the total cost, in dollars, to produce 1000 shirts? (Disregard the $ sign when gridding your answer.)","stimulus":"c of x equals, m x plus 500","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/dfdd66cb65affd3ebcb6128936821e9d3765ad5eced03bf6f192dd06dde4d8f6\" alt=\"c of x equals, m x plus 500\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">A company’s total cost <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc92523ce912e2305a7713864620592ccaaa1af2f6ccb6af0f2099bdbdf0ff9d\" alt=\"c of x\"></span></span>, in dollars, to produce <span class=\"italic \">x</span> shirts is given by the function above, where <span class=\"italic\">m</span> is a constant and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ca09b244cb4a0414885894bc1ac4e0242305210b23d08ccb20204e38d574daf\" alt=\"x is greater than 0\"></span></span>. The total cost to produce 100 shirts is $800. What is the total cost, in dollars, to produce 1000 shirts? (Disregard the $ sign when gridding your answer.)</p>\n","rationale_html":"<p>The correct answer is 3500. The given information includes a cost, $800, to produce 100 shirts. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/48799783206432ce874e94904e85df9834bc3ff1814d51cc8731208ae65b2c85\" alt=\"c of x equals 800 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e89a11a5938631839440ee70e628fad11515b238437b8f95c02c75b11dca3ea5\" alt=\"x equals 100\"></span> into the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1143ec2f74859b2c781dd18d519740b1b59dda1d7be965373cf29cc9b6eb3780\" alt=\"800 equals, m times 100, plus 500 \"></span>. Subtracting 500 from both sides of the equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ff3afaefa4554e3d8f30d6742bbdd9e25bf330f10e5e9664bf133b163b884e24\" alt=\"300 equals, m times 100\"></span>. Dividing both sides of this equation by 100 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0d79671d703d1c631f9f91fa3d5f706de1dbd26ff5b8ebdc68093daa75106d9\" alt=\"3 equals m\"></span>. Substituting the value of <span class=\"italic\">m</span> into the given equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/46cc045d6491d7f7db78a28c6ebfece7ce2147bba917dde1f502054ab8d1f777\" alt=\"c of x equals, 3 x plus 500\"></span>. Substituting 1000 for <span class=\"italic\">x</span> in this equation and solving for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc92523ce912e2305a7713864620592ccaaa1af2f6ccb6af0f2099bdbdf0ff9d\" alt=\"c of x\"></span> gives the cost of 1000 shirts: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/17e474448aeaa6f4ce34f0d26df5e1e94af3256cab284b336c41dc599ad603d9\" alt=\"3 times 1000, plus 500 \"></span>, or 3500.</p>\n","correct_answer":["3500"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.622000+00:00","source_updated_at":"2023-08-02T20:25:59.622000+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}}