Final answer:
The change in the amount of money after Kai and their friends pay a 51 euro bill is represented by -51 euros, indicating a decrease in their total amount of money.
Step-by-step explanation:
When Kai goes out to lunch and receives a bill for 51 euros, the change in the amount of money Kai and their friends have after paying would be represented by option 2): -51 euros. This is because paying the bill results in Kai and their friends' money decreasing by 51 euros. To illustrate, if they had 100 euros before paying for lunch, after they pay the 51 euros, they would have 100 - 51 = 49 euros left, which demonstrates a decrease in the amount of money they possess.