2009 AMC 8 第 23 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。
23.
在学校最后一天，旺德福老师给班上的学生发果冻豆。她给每个男生的果冻豆数等于班上男生人数；给每个女生的果冻豆数等于班上女生人数。她带了 颗果冻豆，发完后剩下六颗。班上男生比女生多两人。她班上有多少名学生？
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
小提示：
设女生人数为 ，则男生人数为
Let the number of girls be so the number of boys is
大提示：
发出的果冻豆总数为
The total jelly beans given out is
解答：
设班上男生人数为 ，女生人数为 。由题意，。
如果每个男生得到 颗果冻豆，那么给所有男生共发出 颗。同样，给所有女生共发出 颗。
因此 因为 不能为负，所以 。这意味着 ，所以 。
所以正确答案是 B。
Let be the number of boys in the class and be the number of girls. From the problem, we get that
If each boy gets jelly beans, then Mrs. Wonderful will give out a total of jelly beans to all the boys. Similarly, she will give out jelly beans to all the girls.
Therefore, Since cannot be negative, we get that This means that so
Thus, B is the correct answer.
其他年份的第 23 题
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