Question

Write a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.An event organizer is reserving rooms for two company-wide events. For the quarterlymeeting this month, she reserved 4 conference rooms and 3 ballrooms, which can seat atotal of 181 attendees. For safety training next month, she reserved 2 conference rooms and3 ballrooms, which can seat 155 attendees. How many attendees can each roomaccommodate?

Answer 1

Given the word problem, we can deduce the following information:

1. For the quarterly meeting this month, she reserved 4 conference rooms and 3 ballrooms, which can seat a total of 181 attendees.

2. For safety training next month, she reserved 2 conference rooms and 3 ballrooms, which can seat 155 attendees.

To determine the number of attendees can each room accommodate, we note first that the system of equations would be:

`\begin{gathered} 4c+3b=181 \\ 2c+3b=155 \end{gathered}`

where:

c = attendees per conference room

b = attendees per ballroom

Now, we use elimination as shown below:

We subtract the 2nd row from the first row:

Next, we solve for c,

`\begin{gathered} 2c=26 \\ c=(26)/(2) \\ c=13 \end{gathered}`

Then, we plug in c=13 into any of the two equations above:

`\begin{gathered} 4c+3b=181 \\ 4(13)+3b=181 \\ Simplify\text{ and rearrange} \\ 52+3b=181 \\ 3b=181-52 \\ 3b=129 \\ b=(129)/(3) \\ Calculate \\ b=43 \end{gathered}`

Therefore, a conference room can accommodate 13 attendees, while a ballroom can accommodate 43 attendees.