A married couple purchased a new car together. Unfortunately, the couple is in the midst of a contentious divorce. They can't agree on what to do with the car, but they do agree to bring in a mediator to help resolve the situation. Below is a chart for what each spouse reports the value of the car to be:

Husband Wife

car $$12,000$ $$18,000$

$($a$)$ Determine the Husband's fair share?

$($b$)$ Determine the Wife's fair share?

Suppose the mediator recommends that the Wife take the car and that she pay the Husband $$8,000.$ Determine if this arrangement is fair for the Husband, the Wife, both, or neither.

The arrangement is fair for both parties

Suppose the mediator recommends that the Wife take the car and that she pay the Husband $$10,000.$ Determine if this arrangement is fair for the Husband, the Wife, both, or neither.

The arrangement is unfair for Wife, but is fair for the other party