Part B.

Each auditorium has both floor seats and balcony seats.
Auditorium A has 250 floor seats and 310 balcony seats and Auditorium B has 195 floor seats and 410 balcony seats. Let f represent the cost of a floor seat and b represent the cost of a balcony seat. If you let R equal total Revenue:

1)Write an equation representing the total possible revenue for Auditorium A.

2)Write an equation representing the total possible revenue for Auditorium B.

3)If both venues sold out for a concert, write an equation representing the total revenue for both venues.

4)If the cost of a floor ticket is $25.90 and the cost of a balcony seat is $12.75, determine the total revenue collected based on your equation from question 3. Show how you arrived at your answer.

5)An event was held using Auditorium A and they only sold floor seats. A total of $5,024.60 was collected. How many floor seats did they sell? Write an equation that models this situation. Show how you arrived at your answer.

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DID DO IT BUT ALL WRONG. HAVE TO DO AGAIN FOR 1/2 CREDIT

1) "Total possible" means maximum revenue. That is what you would get by selling all seats.

For stadium A, that is

R = 250 f + 310 b
Use similar reasoning for the other questions. In some cases you will have to substitute ticket prices for f and b

1) The equation representing the total possible revenue for Auditorium A can be written as:

R_A = f * 250 + b * 310

Explanation: The total revenue for Auditorium A is the sum of revenue from floor seats and revenue from balcony seats. Since there are 250 floor seats with a cost of f and 310 balcony seats with a cost of b, the total revenue can be calculated by multiplying the cost of each type of seat by the number of seats.

2) The equation representing the total possible revenue for Auditorium B can be written as:

R_B = f * 195 + b * 410

Explanation: Similar to Auditorium A, the total revenue for Auditorium B is the sum of revenue from floor seats and revenue from balcony seats. With 195 floor seats and 410 balcony seats, the total revenue is obtained by multiplying the cost of each type of seat with the respective number of seats.

3) If both venues sold out for a concert, the equation representing the total revenue for both venues can be written as:

R_total = R_A + R_B
= (f * 250 + b * 310) + (f * 195 + b * 410)

Explanation: The total revenue from both Auditorium A and Auditorium B is the sum of their individual revenues. By substituting the previously derived equations for R_A and R_B into the equation, we can calculate the total possible revenue.

4) If the cost of a floor ticket is $25.90 and the cost of a balcony seat is $12.75, we can determine the total revenue collected by substituting these values into the equation from question 3:

R_total = (25.90 * 250 + 12.75 * 310) + (25.90 * 195 + 12.75 * 410)
= $6,475 + $5,069.25
= $11,544.25

Explanation: Simply multiply the cost of each type of seat by the respective number of seats for both Auditorium A and Auditorium B. Finally, add up the individual revenues to calculate the total revenue collected.

5) If $5,024.60 was collected from selling only floor seats in Auditorium A, we can write an equation to find the number of floor seats sold. Let x represent the number of floor seats sold:

R_A = f * x = $5,024.60

Explanation: The revenue from selling floor seats in Auditorium A is given by the equation f * x, where f represents the cost of a floor seat and x represents the number of floor seats sold. We can set this equation equal to the given revenue to find the value of x.