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 #104339 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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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?
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\n" ); document.write( "Let x = amt on 1 pile
\n" ); document.write( "Let y = amt in another pile
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\n" ); document.write( "Write an equation for the statement:
\n" ); document.write( "\"33 times the difference of these piles is equal to the difference between the squares of each pile.\"
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\n" ); document.write( "33(x - y) = x^2 - y^2
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\n" ); document.write( "Factor the right side as the difference of squares:
\n" ); document.write( "33(x-y) = (x+y)(x-y)
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\n" ); document.write( "divide both sides by (x-y, and we are left with:
\n" ); document.write( "33 = x + y
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\n" ); document.write( "Any values of x and y that will satisfy this equation will work:
\n" ); document.write( "Three examples
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\n" ); document.write( "x=17,y=16: 33(1) = 17^2 - 16^2 = 33
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\n" ); document.write( "x=20,y=13: 33(7) = 20^2 - 13^2 = 231
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\n" ); document.write( "x=32,y=1: 33(31) = 32^2 - 1^2 = 1023 \r
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