Question

A hotel has 150 rooms. The charges for a double room are $270 per night and $150 per night for a single room. On a night when the hotel was completely occupied. Revenues were $33,300. Which pair of equation can be used to determine the number of double room, d and the number of single room,s,in the hotel?

Answer 1

Step-by-step explanation:

Let s be charges for a single room and d be charges for a double room per night.

We are told that a hotel has 150 rooms. We can represent this information as:

$s+d=150...(1)$

The charges for a double room are $270 per night and $150 per night for a single room. So the charges for s single rooms will be 150s and charges for d double rooms will be 270d.

On a night when the hotel was completely occupied. Revenues were $33,300.

We can represent this information as:  

$150s+270d=33,300...(2)$

Therefore, our desired pair of equations will be:

$s+d=150...(1)$

$150s+270d=33,300...(2)$

Answer 2

Answer: First equation: s+d=150; second equation: 150s+270d=33300

Step-by-step explanation: To solve the given problem we need to write two equations, the first one will express that the total number of rooms is the sum of the single rooms an the double rooms. The second equation will include the sum of the total earnings for the single and double rooms:

First equation:

s+d=150 (the single rooms and the double rooms equal 150 rooms)

second equation:

150s+270d=33300  (the sum of the single and double rooms each one of them multiplied by their prices, equals the total revenue)

To solve the equation we isolate s from the first equation:

s=150-d

and we replace it in the second one:

150(150-d)+270d=33300

solving for d:

22500-150d+270d=33300

120d=33300-22500

120d=10800

d=10800/120

d=90.

now we calculate s from the first equation:

s=150-d

s=150-90

s=60.

There are 60 single rooms and 90 double rooms.