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  3. A certain store sells two types of pens: one type for $2 per pen and the other t

A certain store sells two types of pens: one type for $2 per pen and the other t

游客2025-02-24  1
问题 A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy?
选项 A、9
B、10
C、11
D、12
E、20
答案 D
解析 It is fairly clear that the greatest number of pens that can be bought for $25 will consist mostly, if not entirely, of $2 pens. In fact, it is reasonable to begin by looking at how many of the $2 pens the customer can buy if the customer does not buy any $3 pens. It is easy to see that the customer could buy 12 of the $2 pens, with $1 left over.
    If the customer bought 11 of the $2 pens, there would be $3 left over with which to buy a $3 pen. In this case, the customer could still buy 12 pens.
    If the customer bought 10 of the $2 pens, there would be $5 left over. Only 1 of the $3 pens could be bought with the $5, so in this case, the customer could buy only 11 pens.
    As the number of $2 pens decreases, the total number of pens that the customer can buy with $25 decreases as well. Thus the greatest number of pens the customer can buy with $25 is 12. The correct answer is Choice D.
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