Question

BEN

Ellie is blocking off several rooms in a hotel for guests coming to her wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 6
people. Ellie booked a total of 15 rooms which can accommodate 69 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.

Answer 1

`s+l=15`

`3s+6l=69`

's' represent number of small rooms and 'l' represent number of large rooms.

7 small rooms and 8 large rooms were reserved.

Explanation:

Let the variable 's' represent number of small rooms and 'l' represent number of large rooms.

Given:

Holding capacity of 1 small room = 3 people

Holding capacity of 1 large room = 6 people

Total number of rooms booked = 15

Total number of guests = 69

Using unitary method to get the number of people in 's' small and 'l' large rooms.

∵ 1 small room = 3 people

∴ 's' small rooms =
`3s` people

∵ 1 large room = 6 people

∴ 'l' large rooms =
`6l` people

Now, as per question,

Total rooms = 15

⇒
`s+l=15` ------------------- (1)

Total number of persons = 69

⇒
`3s+6l=69` ------------------- (2)

Therefore, the system of equations that could be used to determine the number of small rooms reserved and the number of large rooms reserved are:

`s+l=15`

`3s+6l=69`

Now, in order to find 's' and 'l', we rewrite equation (1) in terms of 's'. This gives,

`s=15-l`

Now, plug in the value of 's' in equation (2). This gives,

`3(15-l)+6l=69\\45-3l+6l=69\\3l=69-45\\3l=24\\l=(24)/(3)=8\\\therefore s= 15-l=15-8=7`

Therefore, 7 small rooms and 8 large rooms were reserved.