Pearl E$.$ White Orthodontist specializes in correcting misaligned teeth. During $2024,$ Pearl provides services on account of $$575,000.$ Of this amount, $$65,000$ remains receivable at the end of the year. An aging schedule as of December $31,2024,$ is provided below.$$Age GroupAmountReceivableEstimated Percent UncollectibleNot yet due$$25,0005\%0$ to $90$ days past due$14,50010\%91$ to $180$ days past due$9,50030\%$More than $180$ days past due$16,00080\%$Total$$65,000$Required:$1.$Calculate the allowance for uncollectible accounts$\mathrm{.}2.$Record December $31,2024,$ adjusting entry, assuming the balance of Allowance for Uncollectible Accounts before adjustment is $$3,500($credit$)\mathrm{.}3.$On July $19,2025,$ a customers account balance of $$6,500$ is written off as uncollectible. Record the write$-$off$\mathrm{.}4.$On September $30,2025,$ the customer whose account was written off in$$requirement $3$unexpectedly pays the full amount. Record the cash collection.