2. 外语
  3. A certain shop sells 200 bottles of water. All the bottles are sold when the price of each bottle is $2. For every $2 increase i

A certain shop sells 200 bottles of water. All the bottles are sold when the price of each bottle is $2. For every $2 increase i

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问题 A certain shop sells 200 bottles of water. All the bottles are sold when the price of each bottle is $2. For every $2 increase in the price of a bottle of water above $2, the shop will sell 5 fewer bottles, which of the following could be the price of a bottle of water if the revenue from the sale of bottled water is $1,800?
选项 A、$6
B、$8
C、$9
D、$10
E、$18
答案D
解析 这道题目我们可以巧妙地设未知变量。设涨价的次数为x次，则瓶装水单价为2+2x，销量为200-5x，根据单价×销量=收益，可得(2+2x)(200-5x)=1800，整理得x2-39x+140=0；解得x=4或35，所以单价为2+2×4=10美元，或2+2×35=72美元(选项中没有)，因此选择D选项。需要注意的是，有些考生会直接将题目所问的单价设为x，但是这样会让销量的表达式变得复杂，从而使得方程数字较大，容易出现计算失误。所以在设未知量时，应先观察题目中对数量关系的描述，从而设置合适的未知量。
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