The local community theater has fixed expenses of $1500 per week. The theater sells about 150 tickets to a play each week when it charges $20 per ticket. When it charges $14 per ticket, about 210 tickets are sold. Write the equation that relates ticket price and number of tickets sold, and use it to predict how many tickets they should expect to sell if they change the ticket price to $9.50.

Question

amistre64 · Answer

it appears to be linear and they give you two "points" to find the slope with

amistre64 · Answer

teh fixed costs there has no bearing on how many tickets are sold so its just number clutter

amistre64 · Answer

since ticket sales depend on price; equate price to an x value in the equation

amistre64 · Answer

(20,150)  and (14,210) would then be your points to determine slope and the rest with

anonymous · Answer

Ohhhhh I see now

anonymous · Answer

Using those numbers I'd fine the slope intercept? Would that be the answer or more afterwards?

amistre64 · Answer

im assuming they want the equation in slope intercept form; yes.

to find the slope find the ratio of the change in "ticket sales" with respect to a change in "price".

sales move from 150 to 210; thats a change of +60
price moves from 20 to 14; thats a change of -6

the ratio is then 60:-6, or fractionlike 60/-6 = -10

amistre64 · Answer

y = mx-mPx+Py is the format they seem to wanna use soo;  m=-10; and either point will give us the P(x,y) values

amistre64 · Answer

P(20,150) is good enough ....

y = -10x -(-10)(20) + 150  cleans up to what they want I think

anonymous · Answer

Thank you I was just thinking about that process of solving it, you made this a lot clearer for me! :)

amistre64 · Answer

youre welcome; once youve cleaned up the equation; just plug in x=9.50 to determine the number of tickets they would sell at that price :)

anonymous · Answer

Okay, hat clears up the problem for me. You've been a great help.