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 4 people. Hudson reserved twice as many large rooms as small rooms, which altogether can accommodate 66 guests. 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.

Answer 1

To solve the problem, we need to define our variables and set up the equations based on the information provided.

Let's define the variables as follows:

• Let \( s \) be the number of small rooms reserved.
• Let \( l \) be the number of large rooms reserved.

According to the problem, we have the following information:

1. Each small room can hold 3 people, and each large room can hold 4 people.
2. Hudson reserved twice as many large rooms as small rooms, which means \( l = 2s \).
3. The total accommodation capacity provided by both types of rooms equals 66 guests.

From this information, we can write the following equations:

1. For the total accommodation: \[ 3s + 4l = 66 \]

2. For the relationship between small and large rooms: \[ l = 2s \]

Putting it all together, the system of equations is: \[ \begin{cases} 3s + 4l = 66 \ l = 2s \end{cases} \]

This system can be used to determine the values of \( s \) and \( l \).