Recovery Experts $(RE)$ specializes $in$ data recovery from crashed hard drives. The price charged varies based $on$ the extent $of$ damage and the amount $of$ data being recovered. $RE$ offers $a10\%$ discount $to$ students and faculty $at$ educational institutions. Consider the following transactions during the month $of$ June.

June $10$Luke$s$ hard drive crashes and $he$ sends $ittoRE.$June $12$After initial evaluation, $REe-$mails Luke $to$ let him know that full data recovery will cost $$2,400.$June $13$Luke informs $RE$ that $he$ would like them $to$ recover the data and that $heis$ a student $at$ UCLA, qualifying him for $a10\%$ educational discount and reducing the cost $by$ $$240(=$ $$2,40010\%).$June $16RE$ performs the work and claims $tobe$ successful $in$ recovering all data. $RE$ asks Luke $to$ pay within $30$ days $of$ today$s$ date, offering $a2\%$ discount for payment within $10$ days.June $19$When Luke receives the hard drive, $he$ notices that $RE$ did not successfully recover all data. Approximately $30\%of$ the data has not been recovered and $he$ informs $RE.$June $20RE$ reduces the amount Luke owes $by30\%.$June $30$Luke pays the amount owed.