[JSompis]

$\frac{P}{P+Q} = \frac{4}{9}$

$P = \frac{4}{5}Q$


$\frac{Q}{Q+R} = \frac{3}{4}$


$R = \frac{1}{3}Q$


$P+R = 323$

$\frac{4}{5}Q + \frac{1}{3}Q = 323$

$Q = 285$