A stockbroker's commission on a transaction is $2\mathrm{.}5\%$ of the first $$5,000$ of the transaction amount and $1\mathrm{.}5\%$ of the remainder. What was the amount of a transaction that generated a total commission of $$227?$

a$.$ $$11,800\mathrm{.}00$

b$.$ $$10,250\mathrm{.}00$

c$.$ $$12,746\mathrm{.}53$

d$.$ $$23,869\mathrm{.}91$