<PRE><B>Question 709190</B>
a group of students are on sightseeing tour.
the total fare is 120$ and is shared equally among the students.
 if 2 more students join the tour , each will now pay 2$ less.
 find the original number of students in the group.
:
Let n = original number of students
then
(n+2) = two more students
:
{{{120/n}}} - {{{120/((n+2))}}} = 2
multiply n(n+2)
120(n+2) - 120n = 2n(n+2)
120n + 240 - 120n = 2n^2 + 4n
a quadratic equation
0 = 2n^2 + 4n - 240
simplifies to
n^2 + 2n - 120
Factors to 
(n+12)(n-10) = 0
The positive solution
n = 10 is the original number of students
:
:
You can check this yourself
120/10 - 120/12</PRE>