A hotel has 76 rooms & needs to fit 120 guests, how many rooms should be double and how many single?

Question

This is similiar to a question I just asked, but we may need to take some rooms out of service. Single rooms = 1 person, Double rooms = 2 persons each. Thanks!

Answer 1

x = double occupancy rooms
y = single occupancy rooms

x+y=76
2x+y=120

solving for x
x+y=76
x=76-y

we plug this into the other equation

2(76-y)+y=120
152-2y+y=120
152-y=120
-y=-32
y=32

Then we put that back into the first equation

x+32=76
x=44

44 doubles and 32 singles

Answer 2

These are all correct answers. The easiest way to look at it is to know that each room will hold at least one person. Therefore there are 44 people left over if you put one person per room.

120 people - 76 rooms = 44 extra people.

Therefore 44 rooms must be double.

Subtract 44 from the total number of rooms and you have 32 rooms that are singles.

76 rooms-44 doubles=32 singles

Answer 3

Let the number of singles be called 's'.

Let the number of doubles be called 'd'.

The number of rooms is 76, so :-

s + d = 76

There is 1 guest per single room and 2 per double room, and 120 guests in total, so

s + 2d = 120

Put the 2 equations together.

s + d = 76 therefore
s = 76 - d

s + 2d = 120

substituting for s

(76 - d) + 2d = 120

76 + d = 120

d = 120 - 76

d = 44

putting d back into one of the equations to find 's' :-

s = 76 - d
s = 76 - 44
s = 32

Result : s = 32 and d = 44

Answer 4

Let number of single rooms = s and number of double rooms = d

Then s + d = 76
s + 2d = 120

Subtracting 1st equation from the 2nd gives d = 44 whence s = 32

So 44 rooms are double and 32 are single

Answer 5

s+d=76
s+2d=120
subtract 1st from 2nd
d=120-76=44
s=76-44=32

check
32+2*44=32+88=120

Answer 6

44 doubles and 32 singles

Answer 7

It relies upon on the inn, merely start up calling the community lodges you're thinking, and ask what variety of a deal they're prepared to furnish you. And no, it is not too early to try this, October 27 is approximately 8 one million/2 months away, lodges oftentimes start up booking a 365 days beforehand. do slightly analysis first, locate out what the room in many circumstances is going for, locate out if the section caters to by and huge enterprise visitors (meaning weekends the inn is empty) or travelers (meaning the inn is emptier in the time of the week). you may have a fantastically sturdy thought of roughly what number rooms you may assure besides, so verify with all those out of city kinfolk, and notice who's heavily thinking approximately coming, and how many inn rooms could they choose, and for what number nights? i could think of maximum lodges will prefer some variety of deposit to hold the rooms, yet that would probable be paid for by making use of the kinfolk whilst they e book the room. observe there could additionally be an advance in case you may not fill the agreed upon room nights. this could nicely be a reasonably large job too, you may to delegate this one on your mom or dad, or destiny in rules (reckoning on which area many of the out of city travellers are from). acceptable of success to you!

Answer 8

Since history has let it be known that at least 50% of rooms are occupied by at least 2 person's,We'll use that as our basis;

Thus 100 people shall occupy 50 double rooms
20 people shall occupy 20 single rooms and you still have 6 rooms left over for booking agents to sell.

Answer 9

44 doubles and 32 singles

Answer 10

x+y=76
2x+y=120
2x+76-x=120
x=44
y=32
44 double rooms and 32 single rooms