Question 129531
Let {{{n}}} = the number of $1 ticket increases
{{{12 + n}}} is the ticket price
{{{50n}}} is the decrease in attendence for each $1
increase in ticket price
{{{500 - 50n}}} is the attendence for each $1 
increase in ticket price 
{{{(500 - 50n)(12 + n) = 5600}}}
{{{6000 - 600n + 500n - 50n^2 = 5600}}}
subtract 5600 from both sides
{{{400 - 600n + 500n - 50n^2 = 0}}}
Multiply both sides by {{{-1}}}
{{{-400 + 600n - 500n + 50n^2 = 0}}}
{{{50n^2 + 100n - 400 = 0}}}
divide both sides by {{{50}}}
{{{n^2 + 2n - 8 = 0}}}
{{{(n + 4)(n - 2)}}}
{{{n = -4}}}
{{{n = 2}}}
{{{12 + n}}} is the ticket price
The nightly receipts are $5600 when the ticket 
price is $14
check answer:
{{{(500 - 50n)(12 + n) = 5600}}}
{{{500 - 50*2)(12 + 2) = 5600}}}
{{{400*14 = 5600}}}
{{{5600 = 5600}}}
OK