Question 442394
Let {{{x}}} = number of students in original group
The cost per person of the original group was {{{ 360/x }}}
{{{ 360/x - 2 = 360 / ( x + 6 ) }}}
Multiply both sides by {{{ x*( x+6 ) }}}
{{{ 360*(x + 6) - 2*x*(x+6) = 360x }}}
{{{ 360x + 2160- 2x^2 - 12x = 360x }}}
{{{ 2x^2 + 12x - 2160 = 0 }}}
{{{ x^2 + 6x - 1080 = 0 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 6 }}}
{{{ c = -1080 }}}
{{{x = (-6 +- sqrt( 6^2-4*1*(-1080) ))/(2*1) }}}    
{{{x = (-6 +- sqrt( 4356 ))/2 }}}   
{{{x = (-6 +- 66)/2 }}}
{{{x = (-6 + 66)/2 }}} (disregard negative square root)
{{{ x = 30 }}}
There were 30 students in the original group
check:
{{{ 360/x - 2 = 360 / ( x + 6 ) }}}
{{{ 360/30 - 2 = 360 / ( 30 + 6 ) }}} 
{{{ 12 - 2 = 360/36 }}}
{{{ 10 = 10 }}}
OK