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1968 AMC 12 第 34 题

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34.

众议院共有 400400 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 1211\dfrac{12}{11}。第二次投票的赞成票比第一次多多少票？

With 400400 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 1211\dfrac{12}{11} 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?

7575

6060

5050

4545

2020

答案：B
知识点：方程组比与比例
难度评级：1900
小提示：

设第一次和第二次投票的赞成票数分别为 FF 和 GG

Let the original and second numbers voting for be FF and GG

大提示：

使用 G=1211(400−F)G=\frac{12}{11}(400-F) 和 2G−400=2(400−2F)2G-400=2(400-2F)

Use G=1211(400−F)G=\frac{12}{11}(400-F) and 2G−400=2(400−2F)2G-400=2(400-2F)

解答：

设第一次和第二次投票的赞成票数为 FF、GG。由比例条件得 G=1211(400−F)G=\frac{12}{11}(400-F)。通过时的票差是原先落败票差的两倍，所以 2G−400=2(400−2F)2G-400=2(400-2F)，即 G+2F=600G+2F=600。解得 F=180F=180、G=240G=240，所以第二次多了 6060 张赞成票。

因此，正确答案是 B。

Let F,F, GG be the original and second numbers voting for the bill. The ratio condition gives G=1211(400−F).G=\frac{12}{11}(400-F). The passage margin is twice the original defeat margin, so 2G−400=2(400−2F),2G-400=2(400-2F), or G+2F=600.G+2F=600. Solving gives F=180,F=180, G=240,G=240, so 6060 more members voted for it.

Therefore, the correct answer is B.

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