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

anonymous · Answer

Assuming the relationship is linear, the tickets sold seem to go up by 10 every time the price is dropped by $1. E.g.

Tickets Price
150      20
160      19
170      18
180      17
190      16
200      15
210      14
... etc.

The common difference is -10 for the ticket price and, theoretically, if you got down to zero as a price, you would "sell" 350 tickets. Knowing this information can help a great deal in writing the equation.

#Tickets = -10 * Price + 350, or
T=-10P+350 (or T=350-10P makes it a little cleaner)

When the price is 20 dollars, the number of tickets sold would be T=350-10(20)=150

When the price is 14 dollars, the number of tickets sold would be
T=350-10(14)=210

And when the price is 9.50 dollars, the number of tickets sold would be
T=350-10(9.50)=255