document.write( "Question 1031571: A woman bought some large frames for$11 each and some small frames for $7 each at a closeout sale. If she bought 26 frames for $218, find how many of each type she bought. \n" ); document.write( "

Algebra.Com's Answer #646275 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Let the number of large frames be x\r\n" );
document.write( "Let the number of small frames be y\r\n" );
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document.write( "                       Cost      Cost\r\n" );
document.write( "Type       Number       of        of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "frame      frames     frame     frames\r\n" );
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document.write( "large         x        $11       $11x\r\n" );
document.write( "small         y         $7        $7y\r\n" );
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document.write( "TOTALS       26      -----       $218\r\n" );
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document.write( " The first equation comes from the \"number of frames\" column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 26\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \r\n" );
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document.write( "             11x + 7y = 218\r\n" );
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document.write( " So we have the system of equations:\r\n" );
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document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 26\r\n" );
document.write( "               y = 26 - x\r\n" );
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document.write( "Substitute (26 - x) for y in 11x + 7y = 218\r\n" );
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document.write( "  11x + 7(26 - x) = 218\r\n" );
document.write( "   11x + 182 - 7x = 218\r\n" );
document.write( "         4x + 182 = 218\r\n" );
document.write( "               4x = 36\r\n" );
document.write( "                x = 9 = the number of large frames.\r\n" );
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document.write( "Substitute in y = 26 - x\r\n" );
document.write( "              y = 26 - (9)\r\n" );
document.write( "              y = 17 small frames.\r\n" );
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document.write( "Checking:  9 large frames cost $99 and 17 small frames is $119\r\n" );
document.write( "            That's 26 frames.\r\n" );
document.write( "            And indeed $99 + $119 = $218\r\n" );
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document.write( "Edwin

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