document.write( "Question 344976: Divide n into 3 parts such that the first shall be one-rth of the second and one-kth of the third. \n" ); document.write( "
Algebra.Com's Answer #246813 by Edwin McCravy(20060)\"\" \"About 
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Divide n into 3 parts such that the first shall be one-rth of the second and one-kth of the third.
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document.write( "Let x be the first part of n\r\n" );
document.write( "Let y be the second part of n\r\n" );
document.write( "Ley z be the thitrd part of n\r\n" );
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document.write( "Then \r\n" );
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document.write( "x + y + z = n\r\n" );
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document.write( ">>...the first shall be one-rth of the second...<<\r\n" );
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document.write( "x = \"1%2Fr\"*y\r\n" );
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document.write( ">>...the first shall be...one-kth of the third...<<\r\n" );
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document.write( "x = \"1%2Fk\"*z\r\n" );
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document.write( "So we have this system of three equations and three unknowns:\r\n" );
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document.write( "\"system%28x%2By%2Bz=n%2Cx=expr%281%2Fr%29%2Ay%2C+x=expr%281%2Fk%29%2Az%29\"\r\n" );
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document.write( "Clearing the 2nd and 3rd of fractions:\r\n" );
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document.write( "\"system%28x%2By%2Bz=n%2Crx=y%2C+kx=z%29\"\r\n" );
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document.write( "Substituting rx for y and kx for z in the first equation:\r\n" );
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document.write( "\"x%2Brx%2Bkx=n\"\r\n" );
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document.write( "\"%281%2Br%2Bk%29x=n\"\r\n" );
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document.write( "\"x=n%2F%281%2Br%2Bk%29\"\r\n" );
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document.write( "Since \"y=rx\",\r\n" );
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document.write( "\"y=r%2Aexpr%28n%2F%281%2Br%2Bk%29%29\"\r\n" );
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document.write( "\"y=rn%2F%281%2Br%2Bk%29\"\r\n" );
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document.write( "Since \"z=kx\",\r\n" );
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document.write( "\"y=k%2Aexpr%28n%2F%281%2Br%2Bk%29%29\"\r\n" );
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document.write( "\"y=kn%2F%281%2Br%2Bk%29\"\r\n" );
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document.write( "So the parts are\r\n" );
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document.write( "\"n%2F%281%2Br%2Bk%29\", \"rn%2F%281%2Br%2Bk%29\", \"kn%2F%281%2Br%2Bk%29\"\r\n" );
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document.write( "Edwin
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