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Two thirds of the students in a class room are seated in three fourths of the chairs. The rest of the students are punished for not submitting the homework and hence asked to stand. There are $$6$$ empty chairs. The number of persons, that is the number of students including the teacher, in the classroom is
Let the number of students be $$s$$ and the number of chairs be $$c$$. We have $$\frac{2s}{3}=\frac{3c}{4}$$, so $$c=\frac{8s}{9}$$. Since $$6$$ chairs are empty, $$c-\frac{2s}{3}=6$$. Thus $$\frac{2s}{9}=6$$, giving $$s=27$$. Including the teacher, the number of persons is $$28$$.
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