Question 477400
Let {{{ x }}} = number of students who planned to take the trip
given:
the cost per student is {{{ 2500 / x }}}
If 5 more joined the group, the cost per student would be
{{{ 2500/x - 5 }}}
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I can write the equation:
{{{ 2500 / x - 5= 2500/(x + 5)  }}}
Multiply both sides by {{{ x*(x+5) }}}
{{{ 2500*(x+5) - 5x*(x+5) = 2500x }}}
{{{ 2500x + 12500 - 5x^2 - 25x = 2500x
{{{ 5x^2 + 25x - 12500 = 0 }}}
{{{  x^2 + 5x - 2500 = 0 }}}
Using quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -2500 }}}
{{{x = (-5 +- sqrt( 5^2 - 4*1*(-2500) ))/(2*1) }}}
{{{x = (-5 +- sqrt( 25 + 10000 )) / 2 }}}
{{{x = (-5 +- sqrt( 10025 )) / 2 }}}
{{{ x = ( - 5 + 100.125 ) / 2 }}}
{{{ x = 95.125/2 }}}
{{{ x = 47.56 }}}
I can round this to 48 students planned to take the trip
check answer:
{{{ 2500 / (48+5) = 2500/48 - 5 }}}
{{{ 2500/53 = 2500/48 - 5 }}}
{{{ 47.17 = 52.08 - 5 }}}
{{{ 47.17 = 47.08 }}}
This seems close enough
Hope I got it right