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.
We will gladly critique your work and thoughts, if you will make an effort.
he admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 375 people entered the park, and the admission fees collected totaled 1050 dollars. How many children and how many adults were admitted?
1) The equation representing the total possible revenue for Auditorium A can be written as:
R(A) = f * 250 + b * 310
This equation multiplies the cost of a floor seat (f) by the number of floor seats (250) and adds it to the cost of a balcony seat (b) multiplied by the number of balcony seats (310).
2) The equation representing the total possible revenue for Auditorium B can be written as:
R(B) = f * 195 + b * 410
Similarly, this equation multiplies the cost of a floor seat (f) by the number of floor seats (195) and adds it to the cost of a balcony seat (b) multiplied by the number of balcony seats (410).
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)
This equation adds the revenue from Auditorium A to the revenue from Auditorium B to get the total revenue for both venues.
4) To determine the total revenue collected based on the given ticket prices, we substitute the given prices into the equation from question 3:
R(total) = (25.90 * 250 + 12.75 * 310) + (25.90 * 195 + 12.75 * 410)
= 6475 + 3967.5 + 5047.5 + 5247.5
= 20737.50
Therefore, the total revenue collected based on the given ticket prices is $20,737.50.
5) To determine the number of floor seats sold for Auditorium A, we can use the fact that the total revenue collected was $5,024.60. The equation that models this situation can be written as:
5024.60 = f * 250
To solve for f, we divide both sides of the equation by 250:
f = 5024.60 / 250
= 20.10
Therefore, they sold approximately 20 floor seats for Auditorium A.