{"id":"cb_question_bank:c8efc8eb-f976-4ffe-b4a7-a2147b2f7dda","source_id":"cb_question_bank","source_item_id":"c8efc8eb-f976-4ffe-b4a7-a2147b2f7dda","external_id":"ff06a0a2-65a5-41cc-a2c6-f909deb61b07","ibn":null,"question_id":"74c98c82","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An event planner is planning a party. It costs the event planner a onetime fee of dollar sign 35 to rent the venue and dollar sign 10.25 per attendee. The event planner has a budget of dollar sign 200 . What is the greatest number of attendees possible without exceeding the budget?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">An event planner is planning a party. It costs the event planner a onetime fee of <math alttext=\"dollar sign 35\"><mo>$</mo><mn>35</mn>\n</math> to rent the venue and <math alttext=\"dollar sign 10.25\"><mo>$</mo><mn>10.25</mn>\n</math> per attendee. The event planner has a budget of <math alttext=\"dollar sign 200\"><mo>$</mo><mn>200</mn>\n</math>. What is the greatest number of attendees possible without exceeding the budget?</p>","rationale_html":"<p>The correct answer is <math alttext=\"16\"><mn>16</mn>\n</math>. The total cost of the party is found by adding the onetime fee of the venue to the cost per attendee times the number of attendees. Let <math alttext=\"x\"><mi>x</mi>\n</math> be the number of attendees. The expression <math alttext=\"35 plus 10.25 x\"><mn>35</mn><mo>+</mo><mn>10.25</mn><mi>x</mi></math> thus represents the total cost of the party. It's given that the budget is <math alttext=\"dollar sign 200\"><mo>$</mo><mn>200</mn></math>, so this situation can be represented by the inequality <math alttext=\"35 plus 10.25 x less than or equals 200\"><mn>35</mn><mo>+</mo><mn>10.25</mn><mi>x</mi><mo>≤</mo><mn>200</mn></math>. The greatest number of attendees can be found by solving this inequality for <math alttext=\"x\"><mi>x</mi>\n</math>. Subtracting <math alttext=\"35\"><mn>35</mn>\n</math> from both sides of this inequality gives <math alttext=\"10.25 x less than or equals 165\"><mn>10.25</mn><mi>x</mi><mo>≤</mo><mn>165</mn></math>. Dividing both sides of this inequality by <math alttext=\"10.25\"><mn>10.25</mn>\n</math> results in approximately <math alttext=\"x less than or equals 16.098\"><mi>x</mi><mo>≤</mo><mn>16.098</mn></math>. Since the question is stated in terms of attendees, rounding <math alttext=\"x\"><mi>x</mi>\n</math> down to the nearest whole number, <math alttext=\"16\"><mn>16</mn>\n</math>, gives the greatest number of attendees possible.</p>","correct_answer":["16"],"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":[],"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}}