Question 606644: to help out a classmate in need, the students of DCHS section Hope of DCHS decided to send cash aid of Php 2000. Th e students shared the cost equally. At the last minute, 10 chipped in, lowering the cost per person by Php 10 for each student. How many students are there in Section Hope.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 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
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