{"id":"cb_question_bank:b3466f7c-a0c6-4812-8a19-2a325eadb507","source_id":"cb_question_bank","source_item_id":"b3466f7c-a0c6-4812-8a19-2a325eadb507","external_id":"b56c5e06-9287-4cf4-860c-261d954a284d","ibn":null,"question_id":"03503d49","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A business owner plans to purchase the same model of chair for each of the 81 employees. The total budget to spend on these chairs is dollar sign 14,000 , which includes a 7 percent sign sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?","stimulus":"","stimulus_html":null,"stem_html":"

A business owner plans to purchase the same model of chair for each of the 81\n employees. The total budget to spend on these chairs is $14,000\n, which includes a 7\n% sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?

","rationale_html":"

Choice B is correct. It’s given that a business owner plans to purchase 81\n chairs. If p\n is the price per chair, the total price of purchasing 81\n chairs is \n\t81\n\tp\n\n. It’s also given that 7% sales tax is included, which is equivalent to \n\t81\n\tp\n\n multiplied by 1.07\n, or 81(1.07)p. Since the total budget is $14,000, the inequality representing the situation is given by 81(1.07)p≤14,000. Dividing both sides of this inequality by 81(1.07) and rounding the result to two decimal places gives  p≤161.53. To not exceed the budget, the maximum possible price per chair is $161.53.

\n

Choice A is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect. This is the maximum possible price per chair including sales tax, not the maximum possible price per chair before sales tax.

\n

Choice D is incorrect. This is the maximum possible price if the sales tax is added to the total budget, not the maximum possible price per chair before sales tax.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.819000+00:00","source_updated_at":"2023-08-02T20:25:59.819000+00:00","options":[{"label":"A","content_html":"

$148.15

","ord":0},{"label":"B","content_html":"

$161.53

","ord":1},{"label":"C","content_html":"

$172.84

","ord":2},{"label":"D","content_html":"

$184.94

","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}}