So let's call x the number of rooms on each floor, and y the number of floors in the hotel. We have: x*y=60. We also know that the number of rooms on each floor is 4 more than the number of floors, so we have x=y+4. We are looking for the number of rooms on each floor so we should subtract 4 from each side to get x-4=y. We then substitute that back into our original equation and get (x)(x-4)=60. We can solve this two ways: Evalute the factors of 60 or solve the quadratic. The former is quicker because 60 is a small number. We can instantly see that 10 and 6 are two options for x, and we know it's 10 because if it were 6 that would mean the hotel had two floors. If we were to solve the quadratic, we would have:
x²-4x=60 ⇒
x²-4x-60=0 ⇒
(x-10)(x-6)=0 ⇒
x=10 or x=6.
If x=10, that would mean y=6, because x=y+4, which gives us the desired 60 rooms.
If x=6, that would mean y=2, because x=y+4, which gives us an undesired 12 rooms.
There are 10 rooms per floor.
