2021 AMC 12A Spring 第 6 题
先试着解答 2021 AMC 12A Spring 第 6 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2021 AMC 12A Spring 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
6.
一副牌只有红牌和黑牌。随机抽到一张红牌的概率是 。当向这副牌中加入 张黑牌后，抽到红牌的概率变为 。这副牌原来有多少张牌？
A deck of cards has only red cards and black cards. The probability of a randomly chosen card being red is When black cards are added to the deck, the probability of choosing red becomes How many cards were in the deck originally?
小提示：
设红牌数为 ；原牌堆共有 张牌
Let be the number of red cards; the original deck has cards
大提示：
加入 张黑牌后，红牌仍为 张，总数为 ，且比例等于 。
Adding black cards keeps red out of and this equals
解答：
设红牌数为 ，总牌数为 。由 得 。加入 张黑牌后，，所以 。
代入 得 ，因此 ，。
因此，正确答案是 C。
Let be the number of red cards and the total. From we get After adding black cards, so
Substituting gives so and
Thus, the correct answer is C.
其他年份的第 6 题
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