A group of high school students buys a software license for $900. If 5 more students join the group and pay the same amount for the license, each one's contribution is reduced by $9. How many students were originally in the group?
Let's say there were originally x students in the group.
Initially, each student paid $900/x for the software license.
When 5 more students joined the group, the total number of students became x + 5.
Therefore, each student now paid $900/(x + 5) for the software license.
According to the given information, each student's contribution was reduced by $9. So, we can set up the equation:
$900/x - $900/(x + 5) = $9
Solving the above equation, we get:
$900(x + 5) - $900x = $9x(x + 5)
$900x + $4500 - $900x = $9x^2 + 45x
$4500 = $9x^2 + 45x
$9x^2 + 45x - $4500 = 0
$x^2 + 5x - 500 = 0
(x + 25)(x - 20) = 0
Since the number of students cannot be negative, the only valid solution is x = 20.
Therefore, there were originally 20 students in the group.