Question 30720
<pre><b>Let x be the number of $1 increase:
Cost of tickets: x+12
Tickets sold = 500-50x
Equation:
(x+12)(500-50x)=5600
*[tex 500x-50x^2+6000-600x=5600]
*[tex -50x^2-100x+6000=5600]
*[tex -50x^2-100x+400]
Multiply the whole equation by -1 to remove the negative and simplfy:
*[tex 50x^2+100x-400=0]
*[tex x^2+2x-8=0]
Use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=2, c=-8
{{{x=(-2+-sqrt(2^2-4*1*-8))/(2*1)}}}
{{{x=(-2+-sqrt(36))/2}}}
{{{x=(-2-6)/2}}} or {{{x=(-2+6)/2}}}
Remove the negative: and simplfy to get:
x=2

12+2=14
<font color = brown>Hence, it will be $14.</font>
Paul.