Question 838327
Let {{{ n }}} = the number of $1 increases in ticket price:
{{{ 75n }}} = the increase in attendance for {{{ n }}} $1
increases in ticket price
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{{{ 6300 = ( 12 + 1*n )*( 600 - 75n ) }}}
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{{{ 6300 = 12*600 + 600n - 12*75*n - 75n^2 }}}
{{{ 75n^2 + 300n - 900 = 0 }}}
{{{ n^2 + 4n - 12 = 0 }}}
{{{ ( n - 2 )*( n + 6 ) = 0 }}} ( I just guessed at this )
{{{ n = 2 }}} is the answer since {{{ n = -6 }}} won't work
Plugging this back in:
{{{ 6300 = ( 12 + 1*n )*( 600 - 75n ) }}}
{{{ 6300 = ( 12 + 1*2 )*( 600 - 75*2 ) }}} 
{{{ 6300 = 14*450 }}}
{{{ 6300 = 6300 }}}
The nightly ticket price is {{{ 12 + 2 }}} = $14