Weekly Problem 3 - 2010
Let $c$ denote the size of the class and $g$ denote the number of
girls. We want $0.45c< g< 0.5c\Leftrightarrow 0.45<
\frac{g}{c}< 0.5$.
If we try $g=1$ there is no such $c$, since if $c=1$ or $c=2$,
$\frac{g}{c}$ is too large, and if $c> 2$, $\frac{g}{c}$ is too
small.
Similarly for $g=2$, $3$ or $4$. However for $g=5$ setting $c=11$
leads to $\frac{g}{c}=\frac{5}{11}=\frac{500}{11}$%
$=(\frac{440}{11}+\frac{60}{11})$%
$=(40+\frac{55}{11}+\frac{5}{11})$% $=45\frac{5}{11}$%.