jmc

We start with $243=3^5$ cans. After recycling these cans, we will have made $243\cdot \frac{1}{3}=3^4$ new cans. We can then recycle these new cans to make $3^4\cdot \frac{1}{3}=3^3$ new cans. Continuing this process, we want to find the sum $3^4+3^3+3^2+3^1+3^0$. This is a finite geometric series with first term $81$, common ratio $1/3$, and five terms. Thus, the sum is $\frac{81\left(1-{\left(\frac{1}{3}\right)}^5\right)}{1-\frac{1}{3}}=\boxed{121}$.