Han Corp's sales last year were $$485,000,$ and its year$-$end receivables were $$52,500.$ The firm sells on terms that call for customers to pay $30$ days after the purchase, but some delay payment beyond Day $30.$ On average, how many days late do customers pay? Base your answer on this equation: DSO $-$ Allowed credit period $=$ Average days late, and use a $365-$day year when calculating the DSO. Assume all sales to be on credit. Do not round your intermediate calculations.

$10\mathrm{.}18$

$8\mathrm{.}56$

$8\mathrm{.}08$

$9\mathrm{.}51$

$11\mathrm{.}03$