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 syste

Answer 1

To solve the problem, we can define two variables:

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

According to the problem, we have the following information:

1. Each small room can accommodate 3 people, and each large room can accommodate 4 people.
2. Hudson reserved twice as many large rooms as small rooms, which can be expressed as: \[ l = 2s \]
3. The total accommodation provided by these rooms is 66 guests, which can be represented as: \[ 3s + 4l = 66 \]

Now, we can write the system of equations based on this information:

\[ \begin{align*}

1. & \quad l = 2s \
2. & \quad 3s + 4l = 66 \end{align*} \]

This system of equations can be used to determine the number of small rooms \( s \) and large rooms \( l \) reserved by Hudson.