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 $100P+10T+V$ ?

Let's think step by step and output the final answer within \boxed{}.
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