SOLUTION: I got an answer to the following question, but I believe it to be incorrect. I would appreciate an accurate answer! A local playhouse has 200 seats. Records of ticket sales show

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Question 1162030: I got an answer to the following question, but I believe it to be incorrect. I would appreciate an accurate answer!
A local playhouse has 200 seats. Records of ticket sales show that at $24 per ticket, they average 180 seats sold; when tickets are priced at $36, they sell 160 seats, and at $45, only an average of 145 tickets are sold. Make a TABLE to represent this data, then write a linear equation that represents this situation (using point-slope formula).
Based on the linear equation, how much per ticket should the playhouse charge in order to sell all 200 tickets?
Found 4 solutions by josgarithmetic, MathTherapy, greenestamps, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Three points (x,y); x for ticket price, y for average seats sold;
.
and the points (24,180), (36,160), (45,145).
You can make a table if you want.


For these to be on a line, slope ;


In point-slope equation form,
OR
two other possibilities equivalent to this one, since you are given two other points.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

I got an answer to the following question, but I believe it to be incorrect. I would appreciate an accurate answer!
A local playhouse has 200 seats. Records of ticket sales show that at $24 per ticket, they average 180 seats sold; when tickets are priced at $36, they sell 160 seats, and at $45, only an average of 145 tickets are sold. Make a TABLE to represent this data, then write a linear equation that represents this situation (using point-slope formula).
Based on the linear equation, how much per ticket should the playhouse charge in order to sell all 200 tickets?
The other person's equation: , as well as other things are WRONG.

I'll allow you to come up with the correct equation, and when you do, the cost of each ticket, in order to sell out should be  

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


(1) Point-slope is a poor choice for the form of the equation....


(2) There is nothing wrong with the equation shown by the first tutor.  Perhaps they corrected a typo since their initial post.


(3) Note that an equation is not necessary to answer the last question.


The equation is to be linear.  The number of tickets sold drops by 20, from 180 to 160, when the price increases by $12, from $24 to $36.  To INCREASE the number tickets sold by 20, you need to SUBTRACT $12 from the ticket price.


But increasing the number of tickets sold by 20 starting at 180 means all 200 will be sold.  So the price to fill all 200 seats is $24 minus $12, which is $12.


 

Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
 .





            From your post,  I see that you love correctness and precise treatment of Math problems.





            It is  VERY  GOOD  and I like it  (!)





            But let me tell you that you  INCORRECTLY  use the word  (the term)  "average"  in your post.





            So,  I edited your post to make it smooth.  My editing is below.








    A local playhouse has 200 seats. Records of ticket sales show that at $24 per ticket, 
    they  sold 180 seats , in average; 
    when tickets are priced at $36, they sold 160 seats, and at $45, only  145 tickets were sold, in average. 


    Make a TABLE to represent this data, then write a linear equation that represents this situation (using point-slope formula).
    Based on the linear equation, how much per ticket should the playhouse charge in order to sell all 200 tickets?









 

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