- -_business_owner - -_budgets -_$2,200_to_purchase - ~ A small candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?
","rationale_html":"182 The correct answer is . Let s represent the number of small candles the owner , can purchase, and let represent the number of large candles the owner can $4.90 purchase. It’s given that the owner pays per candle to purchase small $11.60 candles and per candle to purchase large candles. Therefore, the owner 4.90 11.60, , pays s dollars for s small candles and dollars for large candles, 4.90 +11.60, which means the owner pays a total of s dollars to purchase $2,200 candles. It’s given that the owner budgets to purchase candles. Therefore, 4.90 +11.60,#2,200 s . It’s also given that the owner must purchase a minimum 200 +,$200 4.90 +11.60,#2,200 of candles. Therefore, s . The inequalities s +,$200 and s can be combined into one compound inequality by rewriting the second inequality so that its left-hand side is equivalent to the left-hand side of , +,$200 the first inequality. Subtracting from both sides of the inequality s $200-, 4.90 yields s . Multiplying both sides of this inequality by yields 4.90 $4.90 200-, 4.90 $980-4.90, 11.60, s ^ h, or s . Adding to both sides 4.90 +11.60,$980-4.90,+11.60, of this inequality yields s , or 4.90 +11.60,$980+6.70, s . This inequality can be combined with the 4.90 +11.60,#2,200 inequality s , which yields the compound inequality 980+6.70,#4.90 +11.60,#2,200 980+6.70,#2,200 s . It follows that . 980 6.70,#1,220 Subtracting from both sides of this inequality yields . Dividing 6.70 ,#182.09 both sides of this inequality by yields approximately . Since the number of large candles the owner purchases must be a whole number, the maximum number of large candles the owner can purchase is the largest whole 182.09 182 number less than , which is .
","correct_answer":["182"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}