In a class, every boy is a friend of exactly three girls and every girl is a friend of exactly two boys . The room only has 19 tables (which can be used by two students maximum) and 31 students in this class are studying French. How many students have this class?

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TopNewestThe ratio of boys to girls must be \(2:3,\) i.e., there will be \(2n\) boys and \(3n\) girls for some integer \(n.\) Thus there will be \(2n + 3n = 5n\) students, so we are looking for a multiple of \(5\) between \(31\) and \(38.\) The only such integer is \(5*7 = 35,\) so there are \(35\) students, \(14\) of whom are boys and \(21\) of whom are girls. – Brian Charlesworth · 2 years ago

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