1993 AIME Problem 10

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\,?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.