Mathematical Problem: Hotel Room Distribution
The image contains a mathematical problem written in Swedish. It states:
"På ett hotell finns dubbelrum med två sängar och enkelrum med en säng. Sammanlagt finns det 80 rum.
En natt var 80% av dubbelrummen och 40% av enkelrummen upptagna. Detta motsvarade 52 rum.
Hur många dubbelsplatsers finns det på hotellet?"
Translated into English, the mathematical problem is as follows:
"At a hotel, there are double rooms with two beds and single rooms with one bed. In total, there are 80 rooms.
One night, 80% of the double rooms and 40% of the single rooms were occupied. This accounted for 52 rooms.
How many double places are there at the hotel?"
To solve this problem, let's use algebra. Let x be the number of double rooms and y be the number of single rooms.
We know two things:
1. The total number of rooms is 80, so x + y = 80.
2. 80% of the double rooms and 40% of the single rooms were occupied, and this accounted for 52 rooms. So 0.8x + 0.4y = 52.
Let's solve this system of equations:
1. x + y = 80.
2. 0.8x + 0.4y = 52.
To eliminate one variable, we could multiply the whole equation (1) by 0.8, which would give us:
0.8x + 0.8y = 64
Now we can subtract this from equation (2):
0.8x + 0.4y = 52
-(0.8x + 0.8y = 64)
----------------------
0 - 0.4y = -12
This simplifies to -0.4y = -12, dividing by -0.4 gives us y = 30.
Now that we know there are 30 single rooms (y), we can substitute this value back into equation (1) to find x:
x + y = 80
x + 30 = 80
x = 80 - 30
x = 50.
There are 50 double rooms at the hotel.
To find out how many double places there are at the hotel, we simply multiply the number of double rooms by the number of beds in each room:
50 double rooms * 2 beds per room = 100 double places at the hotel.
