Question 178713
Let {{{m}}}= current number of members in club
The present cost/person is
{{{20000/m}}}
If 5 more join,
{{{20000/(m+5)}}} will be the cost /person
given:
{{{20000/(m+5) = 20000/m - 2000}}}
Multiply both sides by {{{m*(m+5)}}}
{{{20000m = 20000*(m+5) - 2000*m*(m+5)}}}
{{{20000m = 20000m + 100000 - 2000m^2 - 10000m}}}
{{{2000m^2 + 10000m - 100000 = 0}}}
Divide both sides by {{{2000}}}
{{{m^2 + 5m - 50 = 0}}}
{{{(m + 10)(m - 5) = 0}}}
{{{m = 5}}}
and
{{{m = -10}}} (answer can't be negative)
There are currently 5 members in the club
check:
{{{20000/(m+5) = 20000/m - 2000}}}
{{{20000/(5+5) = 20000/5 - 2000}}}
{{{2000 = 4000 - 2000}}}
{{{2000 = 2000}}}
OK