Shiva's Twin Brother's Triangle

Geometry Level 4

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 $$UXP$$.

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