Question

A hotel 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?

Answer 1

50 rooms with kitchen facilities and 100 rooms without kitchen facilities

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

`y=\frac {1000}{20}=50 rooms`

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

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