Let \(B\) represent boys and \(G\) represent girls. We have \(B+G=300\) and \(2.4B+2.8G=776\). Multiplying the second equation by 10, we get \(24B+28G=7760\), which simplifies to \(6B+7G=1940\). Substituting \(B=300-G\), we get \(6(300-G)+7G=1940\), which simplifies to \(1800-G=1940\), and therefore \(G=140\).
\[
\boxed{140}
\]