SOLUTION: A thousand pounds is divided equally among n people. If there had been 50 people less each person would have received �10 more. Find n

Question 1013329: A thousand pounds is divided equally among n people. If there had been 50 people less each person would have received �10 more. Find n
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A thousand pounds is divided equally among n people.
If there had been 50 people less each person would have received �10 more.
Find n
- = 10
multiply equation by n(n-50)
n(n-50)* - n(n-50)* = 10n(n-50)
Cancel the denominators, you have
1000n - 1000(n-50) = 10n^2 - 500n
1000n - 1000n + 50000 = 10n^2 - 500n
combine like terms, you have a quadratic equation
10n^2 - 500n - 50000 =
simplify divide by 10
n^2 - 50n - 5000 = 0
Factors to
(n - 100)(n + 50) = 0
the positive solution is what we want here
n = 100 people originally
:
:
Check this, find how much each will get
1000/50 = 20 ea
1000/100 = 10 ea
----------------
difference of 10
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