It's party time!

Let $x$ be the original sum of boys and girls at the party. The ratio is $3:7$ , so the total is $3+7=10$ . The original number of boys therefore is $\dfrac{3}{10}x$ and girls is $\dfrac{7}{10}x$ . Then an extra $6$ boys and $2$ girls arrive, so

$\dfrac{\dfrac{3}{10}x+6}{\dfrac{7}{10}x+2}=\dfrac{1}{2}$

Cross multiply.

$\dfrac{6}{10}x+12=\dfrac{7}{10}x+2$

$\dfrac{7}{10}x-\dfrac{6}{10}x=12-2$

$\dfrac{1}{10}x=10$

$x=100$

Total number of girls therefore is $\dfrac{7}{10}(100)+2=$ $\boxed{72}$ .