<PRE><B>Question 800786</B>
For their field studies in marine ecology, a group of students rented a boat for P360. 
However, seven students had to withdraw from the group and as a result, the share of each of the remaining students was increased by P21.00.
 How many students were there in the original group?
:
Let x = no. of students in original group
:
{{{360/x}}} = original price per students
then
{{{360/((x-7))}}} = actual price per student
:
Actual price - original price = 21
{{{360/((x-7))}}} - {{{360/x}}} = 21
multiply by x(x-7) to clear the denominators, resulting in:
360x - 360(x-7) = 21x(x-7)
360x - 360x + 2520 = 21x^2 - 147x
Combine as a quadratic equation
0 = 21x^2 - 147x - 2520
simplify, divide by 21
x^2 - 7x - 120 = 0
Factors to 
(x-15) (x+8) = 0
the positive solution is all we want here
x = 15 students originally
:
:
See if that checks out, find the cost per student
360/8 = 45 (actual)
360/15= 24 (originally)
------------
diff: 21</PRE>