SOLUTION: 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,

Question 1162007: 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 (use point0slope formula).
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 (use point0slope formula).
Let x1=24, y1=180
let x2=45, y2=145
Find the slope using m =
m =
m = reduces to
;
The point/slope form y - y1 = m(x-x1)
y - 180 = (x - 24)
y = x + 40 + 180
y = x + 220 is the linear equation
:
:
Check equation using $36 seats
y = (36) + 220
y = -5(12) + 220
y = -60 + 220
y = 160 seats
Added 7-5-2020-------------------------------------------------------------------------
In case it was you who posted a similar problem where you want to know the cost of a seat when 200 seats are to be filled:
Using the equation we developed above where x is the cost of the seat and y is the number of seats
x + 220 = 200
x = 200 - 220
x = -20
multiply both sides by -3
5x = +60
x = 60/5
x = $12 is cost to fill 200 seats
:
The table would then be
x | y
-------
12 |200
24 |180
36 |160
45 |145
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