请教1数学题

huangfei223

A survey is about seeing three movies.  There are totally 100 people are surveyed.  Among them, 10 saw none of the three movies; those, who saw each of the three movies, are 48, 55, and 47, respectively; and 20 saw all three movies.  How many people saw only two movies?

Answer: 20

咋做呀？谢谢

loxxx

I'm not confident that if I can work it out without knowing in advance the final answer (and I think it's correct).

Here's my approach, by drawing 3 circles overlapping others, and then analyzing the relationship among:

People saw at least 1 movie: 100-10=90

What does (48+55+47) mean? A: number of people saw at least 1 movie with number of people saw 2 movies doubly counted and number of people saw 3 movies triply counted

So 48+55+47-(m+2*20)=90 (m denotes number of people saw 2 movies, while (m+2*20) means the over counted numbers)

Therefore m=20.

[此贴子已经被作者于2009-6-23 0:26:17编辑过]