2010 AMC 8 第 12 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。
12.
一个大袋子里有 个球，其中 是红球，其余是蓝球。必须拿走多少个红球，才能使剩余球中 是红球？
Of the balls in a large bag, are red and the rest are blue. How many of the red balls must be removed so that of the remaining balls are red?
答案：D
小提示：
如果红球占 ，那么蓝球占剩余袋子的
If red balls are , then blue balls are of the remaining bag.
大提示：
蓝球的数量保持不变
The number of blue balls stays fixed.
解答：
若 是红球数，则 因此若 是蓝球数，则
拿走一些球后，如果红球占 ，那么蓝球占 。蓝球数量不变，所以剩余球总数为 。这表示总球数减少了 ，也就是拿走了一百个红球。
所以正确答案是 D。
If is the number of red balls, then Therefore, if is the number of blue balls, then
If there are red balls after removing balls, then there are blue balls. This means the total number of balls is This means the total number of balls decreased by
Thus, the answer is D .
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