2010 AMC 12A 第 5 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。
5.
在一场 箭的射箭比赛进行到一半时，Chelsea 领先 分。每箭射中靶心得 分，其他可能得分为 、、 和 分。Chelsea 每箭至少得 分。如果 Chelsea 接下来 箭都射中靶心，她就能保证获胜。 的最小值是多少？
Halfway through a -shot archery tournament, Chelsea leads by points. For each shot a bullseye scores points, with other possible scores being and points. Chelsea always scores at least points on each shot. If Chelsea’s next shots are bullseyes she will be guaranteed victory. What is the minimum value for
小提示：
Chelsea 的对手在剩下的 箭中每箭最多得 分。
Chelsea’s opponent can score at most points on each of the remaining shots
大提示：
若有 箭靶心，其他 箭至少 分，则需要 。
With bullseyes and at least points on the other shots, require
解答：
对手在最后 箭中最多可得 分。Chelsea 已领先 分，所以她还需要超过 分。
设 Chelsea 有 箭靶心，得 分，其余 箭至少得 分。要保证获胜，需要 化简得 ，即 。
因此至少需要 箭靶心。
所以正确答案是 C。
The opponent can score at most on the last shots. Since Chelsea leads by she must score more than points on her remaining shots to guarantee victory.
Her bullseyes give points, and her other shots give at least points, so This simplifies to i.e.
Therefore Chelsea needs at least bullseyes.
Thus, C is the correct answer.
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