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 
{{{1000/((n-50))}}} - {{{1000/n}}} = 10
multiply equation by n(n-50)
n(n-50)*{{{1000/((n-50))}}} - n(n-50)*{{{1000/n}}} = 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
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difference of 10