Waupaca Company establishes a $$450$ petty cash fund on September $9.$ On September $30,$ the fund shows $$193$ in cash along with receipts for the following expenditures: transportation$-$in$,$ $$54$; postage expenses, $$70$; and miscellaneous expenses, $$124.$ The petty cashier could not account for a $$9$ shortage in the fund. The company uses the perpetual system in accounting for merchandise inventory.

Prepare $(1)$ the September $9$ entry to establish the fund, $(2)$ the September $30$ entry to reimburse the fund, and $(3)$ an October $1$ entry to increase the fund to $$505.$