Reserved Seating: $25.00, 10 rows, 12 seats per row
General Seating: $10.00. 30 rows, 16 seats per row
1. Write a function rule for the amount of seats in the reserved section.
2. What is the revenue of the reserved section?
3. Write a function rule for the amount of seats in the general section.
4. What is the revenue of the general section?
5. What is the total revenue of the building?
6. All the tickets in the reserved section have been sold.
Total revenue from ticket sales will depend on the number of general-seating tickets sold.
Write a function rule to represent the revenue from the reserved section and an unknown amount of tickets from the general section.
Use g as the variable for number of general section tickets and use r for the possible revenue __
Let's address each point step by step:
1. The function rule for the amount of seats in the reserved section can be defined as follows:
\( f(n, m) = n \times m \)
where \( n \) is the number of rows and \( m \) is the number of seats per row.
For the reserved seating section, that is:
\( f_{\text{reserved}}(n, m) = 10 \times 12 \)
2. The revenue of the reserved section can be calculated by multiplying the number of seats in the reserved section by the price per seat:
\( \text{Revenue}_{\text{reserved}} = f_{\text{reserved}}(n, m) \times \text{Price per seat} \)
\( \text{Revenue}_{\text{reserved}} = 10 \times 12 \times 25 \)
3. The function rule for the amount of seats in the general section can be defined similarly to the reserved section:
\( f_{\text{general}}(n, m) = 30 \times 16 \)
4. The revenue of the general section can be found by multiplying the number of seats in the general section by the price per seat:
\( \text{Revenue}_{\text{general}} = f_{\text{general}}(n, m) \times \text{Price per seat} \)
\( \text{Revenue}_{\text{general}} = 30 \times 16 \times 10 \)
5. The total revenue of the building is the sum of the revenues from both sections:
\( \text{Total Revenue} = \text{Revenue}_{\text{reserved}} + \text{Revenue}_{\text{general}} \)
6. To represent the revenue from the reserved section and an unknown amount of tickets from the general section, we can use a function where \( g \) stands for the number of general section tickets sold. Since the revenue from the reserved section is fixed (all tickets have been sold), we only need to consider the variable component for the general section:
\( r(g) = \text{Revenue}_{\text{reserved}} + (g \times \text{Price per general seat}) \)
Let's calculate the actual values for points 2, 4, 5, and the function rule for point 6:
2. Revenue of the reserved section:
\( \text{Revenue}_{\text{reserved}} = 10 \times 12 \times 25 = 3000 \) dollars
4. Revenue of the general section (assuming all seats are sold):
\( \text{Revenue}_{\text{general}} = 30 \times 16 \times 10 = 4800 \) dollars
5. Total revenue (assuming all seats are sold in both sections):
\( \text{Total Revenue} = 3000 + 4800 = 7800 \) dollars
6. Function rule for the revenue from the reserved section and an unknown number of general section tickets:
\( r(g) = 3000 + (g \times 10) \)
where \( r \) is the total possible revenue and \( g \) stands for the number of general section tickets sold.
5. What is the total revenue of the building?
To calculate the total revenue of the building, we add up the revenues from both the reserved and the general sections. Let's calculate them first:
Reserved Section Revenue:
\( \text{Revenue}_{\text{reserved}} = \text{Price per reserved seat} \times \text{Number of reserved seats} \)
\( \text{Revenue}_{\text{reserved}} = \$25.00 \times (10 \text{ rows} \times 12 \text{ seats per row}) \)
\( \text{Revenue}_{\text{reserved}} = \$25.00 \times 120 \)
\( \text{Revenue}_{\text{reserved}} = \$3,000 \)
General Section Revenue (if all seats are sold):
\( \text{Revenue}_{\text{general}} = \text{Price per general seat} \times \text{Number of general seats} \)
\( \text{Revenue}_{\text{general}} = \$10.00 \times (30 \text{ rows} \times 16 \text{ seats per row}) \)
\( \text{Revenue}_{\text{general}} = \$10.00 \times 480 \)
\( \text{Revenue}_{\text{general}} = \$4,800 \)
Total Revenue (with all seats sold in both sections):
\( \text{Total Revenue} = \text{Revenue}_{\text{reserved}} + \text{Revenue}_{\text{general}} \)
\( \text{Total Revenue} = \$3,000 + \$4,800 \)
\( \text{Total Revenue} = \$7,800 \)
Therefore, the total revenue of the building with all seats sold is \$7,800.
Use g as the variable for number of general section
tickets and use r for the possible revenue.
To represent the possible revenue including all of the reserved section tickets and a variable number of general section tickets, we can use the following function rule:
\( r(g) = \text{Revenue from all reserved section tickets} + (\text{Price per general seat} \times g) \)
In this case, we already know that all of the reserved section tickets have been sold, providing a fixed revenue. Let's denote the fixed revenue from the reserved section tickets as \( R_{reserved} \). Let's use \( P_{general} \) as the price per general section ticket.
Now we express \( r \) as a function of \( g \):
\( R_{reserved} = \text{Revenue from all reserved section tickets} \)
\( R_{reserved} = 10 \text{ rows} \times 12 \text{ seats per row} \times \$25 \text{ per seat} \)
\( R_{reserved} = 120 \text{ seats} \times \$25 \text{ per seat} \)
\( R_{reserved} = \$3,000 \)
\( P_{general} = \text{Price per general seat} \)
\( P_{general} = \$10 \)
Therefore, the function for \( r \) given a number of general section tickets \( g \) sold is:
\( r(g) = R_{reserved} + (P_{general} \times g) \)
\( r(g) = \$3,000 + (\$10 \times g) \)
This function rule gives us the possible revenue (represented by \( r \)) for any number of general section tickets sold (represented by \( g \)).
1. To write a function rule for the amount of seats in the reserved section, we need to know how many rows and seats there are.
Since there are 10 rows and 12 seats per row, the function rule is:
Amount of seats in reserved section = 10 rows * 12 seats per row
= 10 * 12
= 120 seats
Therefore, the function rule for the amount of seats in the reserved section is f(x) = 120, where x is the number of seats.
2. To find the revenue of the reserved section, we need to know the price per seat in the reserved section and the total number of seats.
Since the price per seat in the reserved section is $25.00 and there are 120 seats, the revenue of the reserved section is:
Revenue of reserved section = Price per seat * Number of seats
= $25.00 * 120
= $3000.00
Therefore, the revenue of the reserved section is $3000.00.
3. To write a function rule for the amount of seats in the general section, we need to know how many rows and seats there are.
Since there are 30 rows and 16 seats per row, the function rule is:
Amount of seats in general section = 30 rows * 16 seats per row
= 30 * 16
= 480 seats
Therefore, the function rule for the amount of seats in the general section is g(x) = 480, where x is the number of seats.
4. To find the revenue of the general section, we need to know the price per seat in the general section and the total number of seats.
Since the price per seat in the general section is $10.00 and there are 480 seats, the revenue of the general section is:
Revenue of general section = Price per seat * Number of seats
= $10.00 * 480
= $4800.00
Therefore, the revenue of the general section is $4800.00.
5. To find the total revenue of the building, we need to add the revenue of the reserved section and the revenue of the general section.
Total revenue of the building = Revenue of reserved section + Revenue of general section
= $3000.00 + $4800.00
= $7800.00
Therefore, the total revenue of the building is $7800.00.
6. To write a function rule to represent the revenue from the reserved section and an unknown amount of tickets from the general section, we can use the variable g to represent the number of general section tickets and r to represent the possible revenue.
Revenue = Revenue from reserved section + Revenue from general section
= $3000.00 + Price per general section ticket * Number of general section tickets
= $3000.00 + $10.00 * g
Therefore, the function rule to represent the revenue from the reserved section and an unknown amount of tickets from the general section is r(g) = $3000.00 + $10.00 * g, where g is the number of general section tickets.