A tour group of 51 people stayed at a travel agency. The guest rooms in the hotel include double rooms and triple rooms.

List the equation first, and then solve it

Solution: Suppose two people live in room x and three people live in room y.

From the question, we can get {x+y=21 (1)

2x+3y=51 (2)

(1)*2 gets 2x+ 2y=42 (3)

(2)-(3) gets y=9

Put y=9 into (1) and get: x=12

So the explanation of the original system of equations {x=12

y=9

12*39*20=36180=540 (yuan)

Answer: The cost of one night for a tour group is 540 yuan.