Question 606644
The original cost per student = c = 2000/n where n = the number of Section Hope students
The new cost = c - 10 and there are 10 more students:
c - 10 = 2000/(n+10)
So we have 2 equations and 2 unknowns.
Subtract the 2nd from the 1st:
2000/n - 2000/(n+10) = 10
Solve for n:
1/n - 1/(n+10) = 1/200
((n+10) - n)/(n(n+10) = 1/200
n^2 + 10n - 2000 = 0
(n-40)(n+50)
Take the positive solution, n = 40
So the number of students is 40
Check:
2000/40 = 50
2000/50 = 50 - 10 = 40