Algebra Word Problem

Question

A movie theater estimates that for each $0.50 increase in ticket price, the number of tickets sold decreases by 40. The current ticket price of $10.50 yields 1400 tickets sold. Set up and equation to represent the daily revenue. What price should the theater charge for tickets in order to maximize daily revenue?

Answer 1

let x=# of $0.50 increases

(10.5+0.5x)(1400-40x)=0

14,700+700x-420x-20x²=0

14,700+280x-20x²=0

use -b/2a

-280/-40=7

7 fifty-cent increases will maximize revenue

7*$0.50=$3.50

$10.50+$3.50=$14.00 per ticket maximizes revenue

1400-7*40=1400-280=1120 tickets sold

1120*$14.00=$15,680

6 fifty-cent increases gives $13.50*1160=$15,660 which is less money

8 fifty-cent increases gives $14.50*1080=$15,660 also