A tour group of 50 people stayed in a hotel. The hotel's customer service provided three rooms, two rooms, and one room. The three rooms were 20 yuan per person, and the two rooms were 30 yuan per per

A tour group of 50 people stayed in a hotel. The hotel's customer service provided three rooms, two rooms, and one room. The three rooms were 20 yuan per person, and the two rooms were 30 yuan per person.

Warm reminder: It is best to have complete questions, which will help the teacher answer your questions quickly!

Explanation: Suppose three people live in x rooms, and two people live in y rooms, then single rooms live in (20-x-y) rooms, and the total number of people available is 50:

< p>3x+2y+(20-x-y)=50

That is: y=30-2x so 20-x-y=x-10

From x≥0, y≥0, 20-x-y≥0 can be obtained:

x≥0 ①

30-x≥0 ②

x-10≥0 ③

< p>Solution: 10≤x≤15

And x is an integer, so the integer value of x is 10 or 11 or 12 or 13 or 14 or 15.

So the housing There are 6 types of plans: (triple room, double room, single room in order)

①10, 10, 0; ②11, 8, 1; ③12, 6, 2; ④13, 4, 3; ⑤14 , 2, 4; ⑥15, 0, 5

Explanation: ① Only the number of people staying in the room is considered, but the room price is not considered;

② The above situations are all considering the number of people staying in the room. There is room to live in and every room is occupied;

③If every kind of room is required, the two situations ①⑥ will not be considered.