Discussion
In a class of 100 students,
(i) there are 30 students who neither like romantic movies nor comedy movies,
(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and
(iii) the number of students who like both romantic movies and comedy movies is 20.
How many students in the class like romantic movies?
Answer: C
60 students like romantic movies.
Of the 100 students, 30 like neither kind, so 70 like at least one. Let C be the number who like comedy; then \(2C\) like romance and 20 like both. By inclusion and exclusion:
\[ \begin{aligned} 2C + C - 20 &= 70 \\ 3C &= 90 \Rightarrow C = 30 \end{aligned} \]
So \(2C = 60\) students like romantic movies. 30 is the number who like comedy, 40 is the number who like romance only (60 - 20), and 20 is the number who like both.
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