Colorado Rocky Cookie Company offers credit terms to its customers. At the end of $2024,$ accounts receivable totaled $$720,000.$ The allowance method is used to account for uncollectible accounts. The allowance for uncollectible accounts had a credit balance of $$51,000$ at the beginning of $2024$ and $$30,500$ in receivables were written off during the year as uncollectible. Also, $$3,100$ in cash was received in December from a customer whose account previously had been written off. The company estimates bad debts by applying a percentage of $10\%$ to accounts receivable at the end of the year.

$1)$ Prepare journal entries to record the write$-$off of receivables, the collection of $ $3,100$ for previously written off receivables, and the year$-$end adjusting entry for bad debt expense.

$2)$ How would accounts receivable be shown in the $2024$ year$-$end balance sheet?