Question 281982
Let {{{x}}} = current number of members in club
Let {{{C}}} = current cost per person
given:
{{{C = 200000/x}}}
{{{C - 2000 = 200000/(x + 5)}}}
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By substitution:
{{{200000/x - 2000 = 200000/(x + 5)}}}
Multiply both sides by {{{x*(x+5)}}}
{{{200000*(x + 5) - 2000*x*(x+5) =  200000x}}}
{{{200000x + 1000000 - 2000x^2 - 10000x = 200000x}}}
divide both sides by {{{1000}}}
{{{200x + 1000 - 2x^2 - 10x = 200x}}}
{{{2x^2 + 10x - 1000 = 0}}}
{{{x^2 + 5x - 500 - 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{a = 1}}}
{{{b = 5}}}
{{{c = -500}}}
{{{x = (-5 +- sqrt( 5^2-4*1*(-500) ))/(2*1) }}}
{{{x = (-5 +- sqrt( 25 + 2000 ))/2 }}} 
{{{x = (-5 +- sqrt(2025))/2}}}
{{{x = (-5 + 45)/2}}}
{{{x = 20}}} (the negative root is invalid)
There are currently 20 members
check:
{{{C = 200000/x}}}
{{{C = 200000/20}}}
{{{C = 10000}}}
and
{{{C - 2000 = 200000/(x + 5)}}}
{{{10000 - 2000 = 200000/(20 + 5)}}}
{{{8000 = 200000/25}}}
{{{8000 = 8000}}}
OK