Question

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.

Answer 1

x = no of tickets and y = price per ticket then we have

(150,20) and (210,14). We can assume these are linear so

slope = (14-20)/(210-150) = -1/10 and the line is

y = -1/10(x-150) +20 -> y = -x/10 +35

If y = 9.50, then x = -10(9.50 -35) = 255 so

255 tickets may be sold at $9.50.