A school auditorium has $n^{2} + 8n + 15$ seats arranged in a rectangle of $(n+3)$ seats per row. The number…

A school auditorium has $n^{2} + 8n + 15$ seats arranged in a rectangle of $(n+3)$ seats per row. The number of rows is
  1. $n + 5$
  2. $n + 3$
  3. $n + 8$
  4. $n - 5$

Solution

$n^{2}+8n+15 = (n+3)(n+5)$. Rows $= \dfrac{(n+3)(n+5)}{n+3} = n+5$.

Asked in: IMO

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