Well Read

Answer: 7 girls


$b$ boys and $g$ girls, so $\frac{b+g}{3}$ teddy bears.

Books taken out: $$\begin{align}12b+17g+9\times\tfrac{b+g}{3}&=305\\
\Rightarrow 12b+17g+3(b+g)&=305\\ \Rightarrow15b+20g&=305\end{align}$$
Divide through by $5$: $$3b+4g=61$$ $b$ and $g$ must be whole numbers

$3b$	$61-3b$	Divisible by $4$?
$3$	$58$	no
$6$	$55$	no
even multiples of $3$ give odd numbers so only try odd multiples of $3$
$9$	$52$	yes, $4\times13$; $3$ boys and $13$ girls
$15$	$46$	no
$21$	$40$	yes, $4\times10$; $7$ boys and $10$ girls
$27$	$34$	no
go up/down in $12$s (multiple of $4$) not $6$s to hit the multiples of $4$
$33$	$28$	yes, $4\times7$; $11$ boys and $7$ girls
$45$	$16$	yes, $4\times4$; $15$ boys and $4$ girls
$57$	$4$	yes, $4\times1$; $19$ boys and $1$ girl

Also need the number of teddy bears to be an integer so the total number of students is a multiple of $3$

$3+13=16$ no
$7 + 10 = 17$ no
$11 +7=18$ yes
$15+4=19$ no
$19+1=20$ no

So the number of girls is $7$.