Question 982770
One of the costs must be wrong.  Either 210 dollars OR  120 dollars.  Here will stick with 210, but this could be put into another variable for better generality.


m, how many initial members participate
m-5, how many members after five dropout
PRICE initially, 210/m
NEW PRICE, {{{210/m+2}}}


Also the new price is  {{{210/(m-5)}}};


These NEW PRICES must be equal.
{{{highlight(210/m+2=210/(m-5))}}} and what you do is to solve this for m.


What if you say the cost is the variable, c.
Then to solve for m,
{{{highlight_green(c/m+2=c/(m-5))}}}
{{{m(m-5)(c/m+2)=(c/(m-5))(m(m-5))}}}
{{{c(m-5)+2m(m-5)=cm}}}
{{{cm-5c+2m^2-10=cm}}}
cm is shown added to both sides, so add {{{-cm}}};
{{{-5c+2m^2-10=0}}}
{{{2m^2=5c+10}}}
{{{m^2=(5c+10)/2}}}
{{{m=sqrt((5c+10)/2)}}}
{{{m=sqrt((5c+10)/2)(sqrt(2)/sqrt(2))}}}
{{{m=(1/2)sqrt(2(5c+10))}}}
{{{highlight(m=(1/2)sqrt(10c+20))}}}