1950 AMC 12 第 36 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
36.
一位商人以比目录价低 的价格购入商品。他希望设定一个标价，使商品按标价打 的折扣售出后，利润仍为售价的 。标价应为目录价的百分之几？
A merchant buys goods at off the list price. He desires to mark the goods so that he can give a discount of on the marked price and still clear a profit of on the selling price. What per cent of the list price must he mark the goods?
小提示：
设目录价为 ，标价为
Take the list price to be and the marked price to be
大提示：
成本为 ，售价为 ，且成本是售价的
The cost is the selling price is and the cost is of the selling price
解答：
设目录价和标价分别为 和 。商人的成本为 ，打折后的售价为 。利润等于售价的 ，意味着成本是售价的其余 。因此， 所以 ，即目录价的 。
因此，正确答案是 A。
Let the list and marked prices be and The merchant’s cost is while the selling price after the discount is A profit equal to of the selling price means that the cost is the remaining of that price. Therefore Thus or of the list price.
Thus, the correct answer is A.