Answer to Question #168962 in Discrete Mathematics for Trice

Question

In a high school 155 students are surveyed and ask which of the foreign languages they learn.45 learn spanish ,56 learn french,61 learn Chinese.22 learn spanish and french,17 learn spanish and Chinese while 24 learn french and Chinese.9 students don't learn any foreign language. What is the number taking all three subjects

Answer 1

Solution.

Let be $x$ is the number taking all three subjects.

Then $22-x, 17-x, 24-x$ learn only two languages.

So, $6+x$ learn only spanish, $10+x$ learn only french, $20+x$ learn only chinese.

We will have equation

$$9+10+x+6+x+20+x+22-x+17-x+24-x+x=155.$$

From here $x=47.$

But 47 students can not learn three languages because 47>17. This question have not answers. May be the task have an error in condition? If the number of all students will be >108 and <125, the task will be have answer.