Can anyone help me answer this question for my Business law class?

Lucia owns a car dealership, "Lucia's Imports" and pays people such as Jordan a commission if they bring potential customers into the dealership and the customer actually buys a car. For example, if Jordan brings Kali into the dealership and Kali buys a car for $20,000, Lucia pays Jordan $500 as a commission or finder's fee. The people brought into the store, such as Kali, do not know about this arrangement and are just led to believe Jordan and Lucia are friends. You can assume however that the arrangement Lucia and Jordan has is legal.

Jordan brought Durrantt into the dealership and Durrantt bought a car from Lucia. Later Lucia paid Jordan the commission.

About a month later Jordan and Durrantt negotiated the sale of a certain car (details not relevant to the problem) for $20,000. Durrantt gave Jordan a down payment of $5,000 in the form of a check payable to "Jordan for Lucia's Imports". Jordan's bank allowed Jordan to cash the check and Jordan did so and disappeared with the money.

Later Durrantt showed up at Lucia's Imports and said Lucia had to sell him the car and honor the $5,000 down payment he had given to Jordan. Lucia said Jordan was not her agent or employee and she was not legally obligated to honor the purported down payment. Also, Lucia said car's of that type were sold for a minimum of $25,000.

What is the relationship between Lucia and Jordan if it is not principal/agent or employer/employee? Note: This is a separate issue/topic, do not try to discuss this at the same time as the following issue/topic. Use separate paragraphs.

Is Lucia required to honor the "down payment" given to Jordan? Why or why not?