Junior high school math question: Today there is a tour group of 50 people who needs to book 20 rooms. After inquiry, we learned that

(1) Suppose there is a single room X and a double room Y, then the triple room is (20-X-Y)

Then X+2Y+3 (20-X-Y)=50

Deformed to -2X-Y+10=0

①When X=3, Y=4,

②When X=4, Y =2

③When X=5, Y=0

Answer, there are 3 solutions.

(2) The first type: 3×1050×4+(20-3-4)×40=1020

The second type: 4×1050× 2+(20-4-2)×40=1060

The third type: 5×1050×(20-5-0)×40=1200

Answer: When there are 3 single rooms, 4 double rooms, and 13 triple rooms, the minimum fee is 1020