Okay, first of all, I'm writing this while I am battling a major cold so please don't laugh if the Answer jumps out at you.
Let's call this the rental problem.
Both Mark and Pat rent a place together, they each submit $\$775.00$ for the damage deposit for a total of $\$1550.00$.
Mark decides to leave early and break the rental agreement, he suggests that Pat Gives him $\$775.00$ and simply recovers the $\$1550.00$ from the landlord at the end of the lease (assuming Pat decided to live at the same place but with no roommate). One month after Mark leaves, Pat also decides to break the lease which means he must forfeit the whole $\$1550.00$ from the damage deposit account (per the bylaws) In this case, Is Pat out only $ \$1550$ or $\$1550+\$775$ for a total of $\$2325.00$ ?
Thanks in advance :)
Pat initially paid the landlord $\$775$ for his half of the damage deposit. After paying Mark $\$775$, Pat owns the whole damage deposit of $\$1550$. If he doesn't get anything back, Pat has lost that $\$1550$.
But maybe Pat should have consulted a lawyer rather than mathematicians.