Final answer:
Ariana would win if you sued for the remaining $20 because by accepting the check for $30 as a 'full statement,' you agreed to consider the debt settled.
Step-by-step explanation:
In this scenario, it is likely that Ariana would win if you sued for the remaining $20. By accepting the check for $30 as a 'full statement,' you agreed to consider the debt settled. This means Ariana does not owe you any additional money. Although it might seem unfair, legally, accepting the check would be seen as an agreement to release Ariana from the remaining balance.