The December $31,20$X$7$ statement of financial position of Howson Limited showed Trade Accounts Receivable of $$450,000$ and a credit balance in Allowance for Doubtful Accounts of $$45,000.$ During $20$X$8,$ the following transactions occurred: service revenue billed on account, $$1,500,000$; collections from customers, $$1,300,000$; accounts written off $$37,000$; previously written off accounts of $$4,000$ were collected.

Required:

$($a$)$ Record the $20$X$8$ transactions.

$($b$)$ If the company uses the percentage of receivables basis to estimate bad debts expense and determines that uncollectible accounts are expected to be $5\%$ of trade accounts receivable, what is the adjusting entry at December $31,20$X$8?$