my question is in reference to this example problem:

The following information relates to a company's accounts receivable: gross accounts receivable balance at the beginning of the year, $$300,000$; allowance for uncollectible accounts at the beginning of the year, $$25,000($credit balance$)$; credit sales during the year, $$1,500,000$; accounts receivable written off during the year, $$16,000$; cash collections from customers, $$1,450,000.$ Assuming the company estimates bad debts at an amount equal to $2\%$ of credit sales. $1.$ Calculate bad debt expense for the year. $2.$ Calculate the year$-$end balance in the allowance for uncollectible accounts.

bad debt expense $=30,000$

allowance balance $=39,000$

The answer provided above is correct....I just dont understand why you wouldn't plug the estimated uncollectibles into the ending balance of allowance for uncollectible accounts and work basckwards to get the bad debt expense. please see photo for T accounts. Please help me undeerstand. Thanks!