Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 6 people. Hudson booked a total of 19 rooms which can accommodate 87 guests altogether. Write a system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved. Define the variables that you use to write the system.
S = small rooms
L = large rooms
Hudson booked a total of 19 means:
S + L = 19
Which can accommodate 87 guests altogether means:
Small rooms can accommodate 3 people
Large rooms can accommodate 6 people
so
3 S + 6 L = 87
Your system is:
S + L = 19
3 S + 6 L = 87
___________
The solution is:
S = 9 , L = 10
Thanks!
Well, it looks like Hudson is really committed to giving his wedding guests a great experience! Let's break down the information we have and define a couple of variables.
Let's say we have two variables:
- Let's call the number of small rooms reserved "s".
- Let's call the number of large rooms reserved "l".
Now, let's put together the system of equations based on the given information:
- Equation 1: The total number of rooms reserved is 19. So, s + l = 19.
- Equation 2: The total number of guests accommodated is 87. Since a small room can hold 3 people and a large room can hold 6 people, we can write the equation as 3s + 6l = 87.
So, our system of equations is:
s + l = 19
3s + 6l = 87
And that's how we clown around with equations!
Let's denote the number of small rooms reserved as "x" and the number of large rooms reserved as "y".
According to the information given, we can come up with the following equations:
1) The total number of rooms reserved: x + y = 19
2) The total number of guests accommodated: 3x + 6y = 87
These equations represent the number of rooms reserved and the number of guests accommodated.
To write a system of equations, we need to define variables that represent the unknowns in the problem. Let's define:
- Let 's' represent the number of small rooms reserved.
- Let 'l' represent the number of large rooms reserved.
Now, let's set up the equations based on the given information:
1) The total number of rooms reserved:
s + l = 19 ----- Equation (1)
2) The total number of guests that can be accommodated:
3s + 6l = 87 ----- Equation (2)
Equation (1) represents the fact that the total number of rooms reserved, s + l, is equal to 19.
Equation (2) represents the fact that the total number of guests that can be accommodated in the small rooms (3s) and large rooms (6l) is equal to 87.
We now have a system of equations:
s + l = 19
3s + 6l = 87
By solving this system of equations, we can determine the number of small rooms reserved (s) and the number of large rooms reserved (l).