Johnson Company calculates its allowance for uncollectible accounts as $5\%$ of its ending balance in gross accounts receivable. The allowance for uncollectible accounts had a credit balance of $$30,000$ at the beginning of $2024.$ No previously written$-$off accounts receivable were reinstated during $2024.$ At $12/31/2024,$ gross accounts receivable totaled $$500,100,$ and prior to recording the adjusting entry to recognize bad debts expense for $2024,$ the allowance for uncollectible accounts had a debit balance of $55,000.$

Required:

$1)$ What was the balance in gross accounts receivable as of $12/31/2023?$

$2)$ What journal entry should Johnson record to recognize bad debt expense for $2024?$

$3)$ Assume Johnson made no other adjustment of the allowance for uncollectible accounts during $2024.$ Determine the amount of accounts receivable written off during $2024.$

$4)$ If Johnson instead used the direct write$-$off method, what would bad debt expense be for $2024?$