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# Classroom conundrum

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?

Note by Jádson Bráz
2 years, 5 months ago

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## Comments

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The 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.

- 2 years, 5 months ago

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