Combinatorics · Counting · Overlapping sets · Partitions · Ratios · Inequalities
The pupils of a school went to the theatre on two occasions, and every pupil of the school attended at least one of the two performances. Boys formed \(60\%\) of the audience at the first performance and \(75\%\) of the audience at the second. Prove that the school has at least as many boys as girls.
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Serbian Republic Competition (Republicko takmicenje) 1995, high school grade I, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source