Respuesta :
Answer:
[tex]s+l=15[/tex]
[tex]3s+6l=69[/tex]
's' represent number of small rooms and 'l' represent number of large rooms.
7 small rooms and 8 large rooms were reserved.
Step-by-step 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 = [tex]3s[/tex] people
∵ 1 large room = 6 people
∴ 'l' large rooms = [tex]6l[/tex] people
Now, as per question,
Total rooms = 15
⇒ [tex]s+l=15[/tex] ------------------- (1)
Total number of persons = 69
⇒ [tex]3s+6l=69[/tex] ------------------- (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:
[tex]s+l=15[/tex]
[tex]3s+6l=69[/tex]
Now, in order to find 's' and 'l', we rewrite equation (1) in terms of 's'. This gives,
[tex]s=15-l[/tex]
Now, plug in the value of 's' in equation (2). This gives,
[tex]3(15-l)+6l=69\\45-3l+6l=69\\3l=69-45\\3l=24\\l=\frac{24}{3}=8\\\therefore s= 15-l=15-8=7[/tex]
Therefore, 7 small rooms and 8 large rooms were reserved.
