SOLUTION: The total outing cost for a group of people amounted to PhP8000. When an additional four people decided to join the outing, the cost per person decreased by PhP100. How many people

 -  = 100   <<<---===  is the difference in the cost per person.


To solve this equation, multiply both sides by n*(n+4).


8000*(n+4) - 8000n = 100*n*(n+4)


80(n+4) - 80n = n*(n+4)


80n + 320 - 80n = n^2 + 4n


n^2 + 4n - 320 = 0


Factor the polynomial in the left side


(n+20)*(n-16) = 0.


Only positive root n= 16 is meaningful.


Answer.  16 people were there originally in the group.


Check.    -  = 500 - 400 = 100.    ! Correct !