1968 AMC 12 第 34 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。
34.
众议院共有 名议员投票，一项法案未获通过。由同一批议员重新投票后，法案以原先落败票差两倍的票差通过。重新投票时的赞成票数是原先反对票数的 。第二次投票的赞成票比第一次多多少票？
With members voting, the House of Representatives defeated a bill. A re-vote, with the same members voting, resulted in passage of the bill by twice the margin by which it was originally defeated. The number voting for the bill on the re-vote was of the number voting against it originally. How many more members voted for the bill the second time than voted for it the first time?
小提示：
设第一次和第二次投票的赞成票数分别为 和
Let the original and second numbers voting for be and
大提示：
使用 和
Use and
解答：
设第一次和第二次投票的赞成票数为 、。由比例条件得 。通过时的票差是原先落败票差的两倍，所以 ，即 。解得 、，所以第二次多了 张赞成票。
因此，正确答案是 B。
Let be the original and second numbers voting for the bill. The ratio condition gives The passage margin is twice the original defeat margin, so or Solving gives so more members voted for it.
Therefore, the correct answer is B.