document.write( "Question 69240: Please help! I don't know where to begin.\r
\n" ); document.write( "\n" ); document.write( "Question:
\n" ); document.write( "An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.\r
\n" ); document.write( "\n" ); document.write( "So far, this is what I have:
\n" ); document.write( "x + y = $1520
\n" ); document.write( "x(.25) + y(.10)= $1520
\n" ); document.write( "

Algebra.Com's Answer #49282 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
An art dealer sold two artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.
\n" ); document.write( "So far, this is what I have:
\n" ); document.write( "x + y = $1520
\n" ); document.write( "x(.25) + y(.10)= $1520
\n" ); document.write( ":
\n" ); document.write( "That's not quite it. If you assigned the 1st artwork cost as x and the 2nd as y,
\n" ); document.write( "the retail prices would be: 1.25x and 1.10y, so the first scenario equation is:
\n" ); document.write( "1.25x + 1.10y = 1520
\n" ); document.write( ":
\n" ); document.write( "Then the 2nd scenario equation would be:
\n" ); document.write( "1.10x + 1.25y = 1535
\n" ); document.write( ":
\n" ); document.write( "The system of equations;
\n" ); document.write( "1.25x + 1.10y = 1520; multiply eq by 1.10
\n" ); document.write( "1.10x + 1.25y = 1535; multiply eq by 1.25
\n" ); document.write( ":
\n" ); document.write( "1.375x + 1.2100y = 1672
\n" ); document.write( "1.375x + 1.5625y = 1918.75
\n" ); document.write( "----------------------------subtracting eliminates x
\n" ); document.write( "0 -.3525y = -246.75
\n" ); document.write( "y = -246.75/-.3525
\n" ); document.write( "y = $700 is the cost of the 2nd artwork
\n" ); document.write( ":
\n" ); document.write( "Find x using:
\n" ); document.write( "1.25x + 1.1(700) = 1520
\n" ); document.write( "1.25x + 770 = 1520
\n" ); document.write( "1.25x = 1520 - 770
\n" ); document.write( "1.25x = $750
\n" ); document.write( "x = 750/1.25
\n" ); document.write( "x = $600 is the cost of the 1st artwork
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check our solutions in the 2nd scenario equation:
\n" ); document.write( "1.10x + 1.25y = 1535
\n" ); document.write( "1.1(600) + 1.25(700) =
\n" ); document.write( " 660 + 875 = 1535
\n" ); document.write( ":
\n" ); document.write( "
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