document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #629586 by ankor@dixie-net.com(22740)\"\" \"About 
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A thousand pounds is divided equally among n people.
\n" ); document.write( " If there had been 50 people less each person would have received £10 more.
\n" ); document.write( " Find n
\n" ); document.write( "\"1000%2F%28%28n-50%29%29\" - \"1000%2Fn\" = 10
\n" ); document.write( "multiply equation by n(n-50)
\n" ); document.write( "n(n-50)*\"1000%2F%28%28n-50%29%29\" - n(n-50)*\"1000%2Fn\" = 10n(n-50)
\n" ); document.write( "Cancel the denominators, you have
\n" ); document.write( "1000n - 1000(n-50) = 10n^2 - 500n
\n" ); document.write( "1000n - 1000n + 50000 = 10n^2 - 500n
\n" ); document.write( "combine like terms, you have a quadratic equation
\n" ); document.write( "10n^2 - 500n - 50000 =
\n" ); document.write( "simplify divide by 10
\n" ); document.write( "n^2 - 50n - 5000 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(n - 100)(n + 50) = 0
\n" ); document.write( "the positive solution is what we want here
\n" ); document.write( "n = 100 people originally
\n" ); document.write( ":
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\n" ); document.write( "Check this, find how much each will get
\n" ); document.write( "1000/50 = 20 ea
\n" ); document.write( "1000/100 = 10 ea
\n" ); document.write( "----------------
\n" ); document.write( "difference of 10 \n" ); document.write( "
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