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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
admin
2019-05-11
40
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x
2
-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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