In a class of 100 students, 30 like neither romantic movies nor comedy movies. The number who like romantic movies is twice the number who like comedy movies, and 20 like both. How many like romantic movies?
The union has 100−30=70 students. If C like comedy, then 2C like romantic movies. Inclusion–exclusion gives 2C+C−20=70, hence C=30 and the romantic-movie count is sixty. Choose C; students liking both are included in each category.
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