Sure, let's break down the problem step-by-step.
Defining the Variables:
Let [tex]\(x\)[/tex] be the number of movie tickets.
Writing the Equations:
1. Cineplex Movie Charges:
- Cineplex has a base charge of [tex]$20 per month.
- Additionally, they charge $[/tex]5 per movie ticket.
- Therefore, the total cost for Cineplex can be represented as:
[tex]\[
C = 20 + 5x
\][/tex]
where [tex]\(C\)[/tex] is the total cost for Cineplex.
2. Sony Theatre Charges:
- Sony Theatre has a base charge of [tex]$40 per month.
- Additionally, they charge $[/tex]3 per movie ticket.
- Therefore, the total cost for Sony Theatre can be represented as:
[tex]\[
S = 40 + 3x
\][/tex]
where [tex]\(S\)[/tex] is the total cost for Sony Theatre.
So the system of equations that models this problem is:
[tex]\[
\begin{cases}
C = 20 + 5x \\
S = 40 + 3x
\end{cases}
\][/tex]
This system of equations represents the total monthly costs for both Cineplex Movie and Sony Theatre based on the number of movie tickets [tex]\(x\)[/tex].
