SEAMO 2027 - Paper E - SET 09 - Self-study Question 24

In triangle $ABC$, $M$ lies on $AC$, $N$ lies on $AB$, and $BM,CN$ intersect at $P$ as shown. Given areas $[CMP]=3$, $[BNP]=4$, $[BCP]=5$, find $[ABC]$. Brackets denote area.