Question 1056296
The Extreme Rock Climbing Club planned a climbing expedition.  The total cost was $2600<s>$2600</s>, which was to be divided equally among the members going.  Prior to the trip, 1010 members decided not to go.  If the cost per person increased by $130<s>$130</s>, how many people went on the expedition?
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Let c be the original number of climbers planning to go.



Original PRICE,  {{{2600/c}}} dollars per member;


New price if 1010 members decided not to go, {{{2600/(c-1010)}}}.  This is given as  130 dollar per person increase.
{{{highlight_green(2600/(c-1010)-2600/c=130)}}}


{{{20/(c-1010)-20/c=1}}}


{{{20(c)-20(c-1010)=c(c-1010)}}}


{{{20c-20c+20200=c^2-1010c}}}


{{{20200=c^2-1010c}}}


{{{c^2-1010c-20200=0}}}


Check the discriminant.
{{{(1010)^2+4*20200}}}
{{{1020100-80800}}}
{{{939300}}}----the discriminant....
{{{9393*10^2}}}
{{{3*3131*10^2}}}------discriminant plainly is NOT a perfect square and solution of c will NOT be a whole positive number.


{{{c=(1010+- 10*sqrt(9393))/2}}}


{{{c=202+- 5*sqrt(9393)}}}, the minus form will not work.


{{{c=202+5*(96.9175)}}}


{{{c=686.6}}}


Most useful original number of planned climbers were  687 club members.