蓝书上206页478题

chongov

478. Four extra-large sandwiches of exactly the same size were ordered for m students, where m>4. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
正确答案（E）(4m-12)/m(m-4)

这道题我凭自己的直觉猜对了【因为其中貌似有个3，又想到4m-12=4（m-3）】
但不知道具体解题过程应如何进行
望各位给予解答

danoulini

假设每个sandwich重A公斤（这个其实不一定需要，只是帮助理解）

先说那三块：每个人分了3A/m公斤
再说那一块：除了那4个人外，其他人都分了A/（m-4）公斤

Carol肯定不在后面这伙儿人中，所以Carol分了3A/m + A/（m-4）公斤
所以他分得的百分比：[3A/m + A/（m-4）] / A = 你给的那个答案

chongov

理解了，谢谢