<PRE><B>Question 390123</B>
Tickets to a school dance cost $5.00, and the projected attendance is 300 people. For every $0.50 increase in the ticket price, the dance committee projects that attendance will decrease by 20. What ticket price will generate $1562.50 in revenue?
:
Let x = no. of .50 increases
Let x = no. of 20 people decreases
:
(5 + .5x)(300 - 20x) = 1562.50
FOIL
1500 - 100x + 150x - 10x^2 = 1562.5
A quadratic equation
-10x^2 + 50x + 1500 - 1562.5 = 0
:
-10x^2 + 50x - 62.5 = 0
Solve this using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=-10; b=50; c=-62.5
{{{x = (-50 +- sqrt( 50^2-4*-10*-62.5 ))/(2*-10) }}}
:
{{{x = (-50 +- sqrt(2500 - 2500 ))/(-20) }}}
x = {{{(-50)/(-20)}}}
x = 2.5
:
Ticket price: 2.5(.5) + 5.00 = $6.25
:
No. of ticket: 300 - 2.5(20) = 250 people
:
Revenue: $6.25 * 250 = $1562.5
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