Question 176375
Let {{{x= number _of_ current_ members}}}.

Current cost per person is {{{C = 200000/x}}}.

Cost per person with new members will be {{{C= 200000/(x + 5)}}}.

Solve for {{{x}}}:

{{{200000/x - 2000 = 200000/(x + 5)}}}

Multiply through by {{{x(x + 5)}}}:
{{{200000(x + 5) - 2000x(x + 5) = 200000x}}}


Divide through by {{{2000}}}:

{{{200000(x + 5)/2000 - 2000x(x + 5)/2000 = 200000x}}}


{{{100(x + 5) - x(x + 5) = 100x}}}

Simplify:

{{{100x + 500 - x^2 - 5x = 100x}}}

{{{ -x^2 - 5x + 500 = 0}}}.....multiply by {{{-1}}}

{{{ x^2 + 5x - 500 = 0}}}

{{{(x + 25)(x - 20) = 0}}}

{{{x = -25}}} and {{{x=20}}}…you will need only positive root, so throw out the negative value.

There are {{{20}}} members currently.