Can you help me with this one?
Each auditorium has both floor seats, and balcony seats. Auditoruim A has 200 floor seats and 500 balcony seats. Auditorium B has 100 floor seats and 200 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.
Question one: write an equation representing the total possible revenue for auditorium A: I answered 200f+500b=r
Question 2: write an equation representing the total possible revenue for auditorium b. I answered: 100f+200b=r
Question 3:If both venues sold out for a concert , write an equation representing the total revenue of both venues. I answered : 300f+700b=r
Question 4: If the cost of a floor seat is 22.75 and the cost of a balcony seat is 10.50 determine the total revenue collected based on your equation in question 3. I answered : 300(22.75)+700(10.50)=r r=14,175.00
Question 4:An event was held using auditorium A, and they sold only floor seats. A total of 3981.25 was collected . How many floor seats did they sell. Write an equation that models this situation. I answered: 200f=3981.25 with a solution of 19.90625
Are these answers right if not can you help me with this one?
All correct, except the second question 4.
You know: "auditorium A, and they sold only floor seats. A total of 3981.25 was collected"
In your answer, you made f into a variable, and that answer would be right if f was variable and if they had sold all 200 seats.
However, f is not variable. f - the cost of a floor seat - is always 22.75.
The problem is not to find the cost of the seat; it's to find how many seats, @ 22.75 each, were sold. So try the question again, keeping that in mind.
Hint: they didn't sell all 200.
22.75f=3981.25
dividing 22.75 by both sides I get 175 for the answer. is that right?
Yes!
Thank you so much for your help, it was greatly appreciated
Afterthought: careful with that lettter!
You don't want to use f again, because the variable you're looking for is not the price of a seat. f has already been used for the price, so using it for the number of seats is confusing.
Pick another variable, like x.
Then
22.75x = 3981.25
x = 175
I noticed that too...thanks again!
Your answers to questions 1, 2, and 3 are correct.
For question 4, to determine the total revenue collected based on the equation in question 3, you need to substitute the given values for the cost of a floor seat (22.75) and the cost of a balcony seat (10.50) into the equation. Therefore, the correct calculation would be:
Total revenue = 300(22.75) + 700(10.50) = 6825 + 7350 = 14,175.
So your answer is correct for question 4.
For question 5, to model the situation where only floor seats were sold in auditorium A, you should modify the equation representing the total revenue for auditorium A. Since only floor seats were sold, the revenue would be equal to the cost of a floor seat (f) multiplied by the number of floor seats sold. The equation can be written as:
200f = 3981.25
To solve this equation, divide both sides by 200:
f = 3981.25 / 200 = 19.90625
So, your answer for the number of floor seats sold in question 5 is correct as well.