Shiva's Twin Brother's Triangle

In the diagram, points $X, Y, Z$ are on the sides of triangle $UVW$ , as shown. Line segments $UY, VZ, WX$ intersect at point $P$ . Point $Y$ is on $VW$ such that $VY : YW = 4 : 3$ . If triangle $PYW$ has an area of $30$ and triangle $PZW$ has an area of $35$ , determine the area of triangle $UXP$ .