Answer
The amount of calla lilies bought is $7$, and the amount of peonies bought is $15$.
Work Step by Step
Let $x$ be amount of calla lilies bought. Then the amount of peonies bought is $12-x$. Then our equation is: $3.5x+(12-x)5.5=52\\3.5x+66-5.5x=52\\2x=14\\x=7$.
The amount of calla lilies bought is $7$, and the amount of peonies bought is $15$.