Question 22160
Let number of student originally = x
Therefore number of students who actually turn up = x-5


Original cost per head = 500/x whereas the actual Cost per head = 500/(x-5)


Now, the actual cost (per head) - original cost (per head) = 5. So,


{{{500/(x-5) - 500/x = 5}}}. Now get rid of the fractions by multiplying every term by x(x-5). Some cancelling happens and we are left with:


500x - 500(x-5) = 5x(x-5).


We need to multiply this out, collect terms and then solve the resulting quadratic:


{{{500x - 500x + 2500 = 5x^2 - 25x)}}}
{{{2500 = 5x^2 - 25x)}}}
{{{5x^2 - 25x - 2500 = 0)}}}
{{{x^2 - 5x - 500 = 0)}}}
(x + 20)(x - 25) = 0


so either x+20 = 0 OR x-25 = 0
so either x = -20 or x = 25


As x is the number of students, we cannot have a negative, so the answer we require is 25.


CHECK:
500/25 --> $20 per head


then down to 20 students, 500/20 --> $25 per head.


So this is correct, the price did increase by $5 per head.


jon.