Cutler Education Corporation developed a software product to help children under age $12$ learn mathematics. The software contains two separate parts: Basic Level $($Level I$)$ and Intermediate Level $($Level II$).$ Parents purchase each level separately and are eligible to purchase the access code for Level II only if their children pass the Level I exam.

Kerry purchases the Level I software at a price of $$50$ for his son, Tom, on December $1.$ Suppose Tom passed the Level I test on December $10,$ and Kerry immediately purchased the access code for Level II for an additional $$30.$ Cutler provided Kerry with the access code to Level II on December $20.$