OG详解-OG2 数学1 Q14

The correct answer is 182. Let s represent the number of small candles the owner can purchase, and let L represent the number of large candles the owner can purchase. It’s given that the owner pays  $4.90  per candle to purchase small candles and $11.60  per candle to purchase large candles. Therefore, the owner pays 4.90s  dollars for s  small candles and 11.60L  dollars for L large candles, which means the owner pays a total of  4.90s +11.60L dollars to purchase candles. It’s given that the owner budgets  $2,200  to purchase candles.Therefore, 4.90s +11.60L  ≤2,200 . It’s also given that the owner must purchase a minimum of 200 candles. Therefore,  s + L ≥200 . The inequalities 4.90s +11.60L ≤2,200 and s + L≥200  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 the first inequality. Subtracting L from both sides of the inequality s + L≥200 yields s ≥ 200 -L . Multiplying both sides of this inequality by 4.90  yields 4.90s ≥4.90 ( 200-L), or 4.90s ≥980 -4.90L. Adding 11.60L  to both sides of this inequality yields 4.90s +11.60L ≥980-4.90L +11.60L , or 4.90s +11.60L ≥980 +6.70L . This inequality can be combined with the inequality 4.90s +11.60L ≤2,200, which yields the compound inequality 980 +6.70L ≤4.90s +11.60L ≤2,200 . It follows that 980 +6.70L≤2,200. Subtracting 980  from both sides of this inequality yields  6.70L ≤2,200. Dividing both sides of this inequality by  6.70 yields approximately  L ≤182.09. 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 numberless than 182.09 , which is 182.