Ahotel has 150 rooms. those with kitchen facilities rent for $100 per night in those without kitchen facilities rent for $80 per night. on a night when the hotel was completely occupied, revenues were $13,000. how many of each type of room does the hotel have?

50 rooms with kitchen facilities and 100 rooms without kitchen facilities

Step-by-step explanation:

Let the rooms without kitchen facilities be x and those with kitchen facilities be y

Form set of equations

Since the total rooms are 15, then the first equation is

x+y=150

Therefore, x=150-y

Considering the cost of rooms and what was collected, then

80x+100y=13000

Substituting x with 150-y then

80(150-y)+100y=13000

12000-80y+100y=13000

20y=1000

Therefore, x=150-y=150-50=100 rooms

Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities