SOLUTION: A community theater sells about 150 tickets to a play each week when it charges $20 per ticket. For each $1 decrease in price, about 10 more tickets per week are sold. The theater

Question 190088: A community theater sells about 150 tickets to a play each week when it charges $20 per ticket. For each $1 decrease in price, about 10 more tickets per week are sold. The theater has fixed expenses of $1500 per week.
Write a model: write a verbal model and a quadratic function to represent the theater's weekly profit.
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What i did is this, but I am not sure if I am right:
y=(-x+20)(10x+150)-1500
y=-10x^2-150x+200x+3000-1500
y=-10x^2+50x+1500
I really don't understand how to create equations out of word problems like this. I really appreciate the help.. Thank You !
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Yep, that's exactly right as long as you realize that your independent variable represents the price differential. In other words, the actual price of a ticket is 20 - x.

That means you have some restrictions on the domain of your function. For one thing, x has to be less than 20 (unless the play is so bad they have to pay people to attend) and x has to be less than 35 or they would sell zero tickets.

John

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