document.write( "Question 69240: Please help! I don't know where to begin.\r
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document.write( "Question:
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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
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document.write( "So far, this is what I have:
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document.write( "x + y = $1520
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document.write( "x(.25) + y(.10)= $1520 \n" );
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Algebra.Com's Answer #49282 by ankor@dixie-net.com(22740)![]() ![]() 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( " \n" ); document.write( " |