Final answer:
The greatest amount of money Jenny could have is $2.
Step-by-step explanation:
In order to find the greatest amount of money Jenny could have, we need to consider the highest value coins she could have. The highest value coin in circulation is the dollar coin. Let's assume she has all dollar coins in her purse. Since she's unable to make change for a 2 dollar bill, the greatest amount of money she could have is $2.