Answer :
To solve the problem, we need to set up a system of equations based on the information provided about ticket sales at the movie theater.
1. Identify the Variables:
- Let [tex]\( f \)[/tex] be the number of full-price tickets sold.
- Let [tex]\( r \)[/tex] be the number of reduced-price tickets sold.
2. Translate the Information into Equations:
- We know the total number of tickets sold is 214. So, we can express this as:
[tex]\[
f + r = 214
\][/tex]
- The total revenue from selling these tickets is \[tex]$2,145. We also know the price per ticket:
- Full-price ticket: \$[/tex]11 each
- Reduced-price ticket: \$8.25 each
- The revenue equation using the ticket prices becomes:
[tex]\[
11f + 8.25r = 2145
\][/tex]
3. System of Equations:
With the two equations identified, we have the system:
- Equation 1: [tex]\( f + r = 214 \)[/tex]
- Equation 2: [tex]\( 11f + 8.25r = 2145 \)[/tex]
This system of equations will allow us to solve for the number of full-price tickets [tex]\( f \)[/tex] and reduced-price tickets [tex]\( r \)[/tex] sold.
The correct system of equations is:
- [tex]\( f + r = 214 \)[/tex]
- [tex]\( 11f + 8.25r = 2145 \)[/tex]
This setup will help find out how many of each type of ticket were sold to achieve the total revenue and the total ticket sales.
1. Identify the Variables:
- Let [tex]\( f \)[/tex] be the number of full-price tickets sold.
- Let [tex]\( r \)[/tex] be the number of reduced-price tickets sold.
2. Translate the Information into Equations:
- We know the total number of tickets sold is 214. So, we can express this as:
[tex]\[
f + r = 214
\][/tex]
- The total revenue from selling these tickets is \[tex]$2,145. We also know the price per ticket:
- Full-price ticket: \$[/tex]11 each
- Reduced-price ticket: \$8.25 each
- The revenue equation using the ticket prices becomes:
[tex]\[
11f + 8.25r = 2145
\][/tex]
3. System of Equations:
With the two equations identified, we have the system:
- Equation 1: [tex]\( f + r = 214 \)[/tex]
- Equation 2: [tex]\( 11f + 8.25r = 2145 \)[/tex]
This system of equations will allow us to solve for the number of full-price tickets [tex]\( f \)[/tex] and reduced-price tickets [tex]\( r \)[/tex] sold.
The correct system of equations is:
- [tex]\( f + r = 214 \)[/tex]
- [tex]\( 11f + 8.25r = 2145 \)[/tex]
This setup will help find out how many of each type of ticket were sold to achieve the total revenue and the total ticket sales.
