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Let's denote:
- R as the number of students who like romantic movies,
- C as the number of students who like comedy movies.
We know:
- There are 30 students who neither like romantic nor comedy movies.
- The number of students who like romantic movies is twice the number of students who like comedy movies, so R = 2C.
- The number of students who like both romantic and comedy movies is 20.
We can set up an equation using the principle of inclusion-exclusion: Total students = R + C - (students who like both romantic and comedy movies) + (students who like neither romantic nor comedy movies).
Substituting the given values: 100 = R + C - 20 + 30.
Since R = 2C, we can substitute R with 2C in the equation: 100 = 2C + C - 20 + 30.
Now, solving for C: 100 = 3C + 10.
Subtracting 10 from both sides: 90 = 3C.
Dividing both sides by 3: C = 30.
Now, substituting the value of C back into R = 2C: R = 2 * 30, R = 60.
So, there are 60 students in the class who like romantic movies.