Homework Help Forum: Algebra

Posted by newcomb on Thursday, November 5, 2009 at 8:19pm.

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?

• Algebra - TeacherJim, Thursday, November 5, 2009 at 8:35pm

  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.

  
  

• Algebra - newcomb, Thursday, November 5, 2009 at 8:59pm

  22.75f=3981.25 dividing 22.75 by both sides I get 175 for the answer. is that right?

  
  

• Algebra - TeacherJim, Thursday, November 5, 2009 at 9:08pm

  Yes!

  
  

• Algebra - newcomb, Thursday, November 5, 2009 at 9:10pm

  Thank you so much for your help, it was greatly appreciated

  
  

• Algebra - TeacherJim, Thursday, November 5, 2009 at 9:11pm

  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

  
  

• Algebra - newcomb, Thursday, November 5, 2009 at 9:13pm

  I noticed that too...thanks again!

  
  

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