Euler's formula states that for a convex polyhedron with \(V\,\) vertices, \(E\,\) edges, and \(F\,\) faces, \(V-E+F=2\,\). A particular convex polyhedron has 32 faces, each of which is either a triangle or a pentagon. At each of its \(V\,\) vertices, \(T\,\) triangular faces and \(P^{}_{}\) pentagonal faces meet. What is the value of \(100P+10T+V\,\)?

(第十一届AIME1993 第10题)