document.write( "Question 143309: A man divides his gold coins into two piles. 33 times the difference of these piles is equal to the difference between the squares of each pile. How many in each pile? \n" ); document.write( "

Algebra.Com's Answer #104338 by ptaylor(2198) $\"\"$ $\"About$

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\n" ); document.write( "Let x=number of pieces in the large pile
\n" ); document.write( "And let y=number of pieces in the small pile\r
\n" ); document.write( "\n" ); document.write( "33(x-y)=33 times the difference of these piles
\n" ); document.write( "x^2-y^2=the difference between the squares of each pile\r
\n" ); document.write( "\n" ); document.write( "So our equation to solve is:
\n" ); document.write( "33(x-y)=x^2-y^2
\n" ); document.write( "Note that x^2-y^2=(x-y)(x+y) so we now have
\n" ); document.write( "33(x-y)=(x-y)(x+y) divide each side by (x-y); recognizing that (x-y) not equal to zero\r
\n" ); document.write( "\n" ); document.write( "x+y=33
\n" ); document.write( "x=32, y=1
\n" ); document.write( "x=31, y=2
\n" ); document.write( "x=30, y=3
\n" ); document.write( "x=29, y=4
\n" ); document.write( "etc.
\n" ); document.write( "etc.
\n" ); document.write( "etc.
\n" ); document.write( "---
\n" ); document.write( "---
\n" ); document.write( "x=18, y=15
\n" ); document.write( "x=17, y=16\r
\n" ); document.write( "\n" ); document.write( "Any of the above combinations of piles work.
\n" ); document.write( "----interesting problem-----
\n" ); document.write( "Hope this helps---ptaylor\r
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