document.write( "Question 1166874: A certain brand of pencils comes in three packages with 6, 12, and 24 pencils, costing Php 2.00, Php 3.00 and Php 4.00 per package, respectively. A store sold 12 packages containing a total of 162 pencils, and took in Php 35.00. How many 12 package were sold? \n" ); document.write( "

Algebra.Com's Answer #791421 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "A certain brand of pencils comes in three packages with 6, 12, and 24 pencils, costing Php 2.00, Php 3.00 and Php 4.00
\n" ); document.write( "per package, respectively. A store sold 12 packages containing a total of 162 pencils, and took in Php 35.00. How many 12 package were sold?
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document.write( "Let x = # of 6-pencils packages\r\n" );
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document.write( "    y = # of 12-pencils packages\r\n" );
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document.write( "    z = # of 24-pencils packages\r\n" );
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document.write( "Then from the condition, you have these 3 equation for 3 unknowns\r\n" );
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document.write( "     x +  y  +   z =  12    (1)\r\n" );
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document.write( "    6x + 12y + 24z = 162    (2)\r\n" );
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document.write( "    2x +  3y +  4z =  35    (3)\r\n" );
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document.write( "In equation (2), cancel the common factor 6 in both sides\r\n" );
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document.write( "     x +  y  +   z =  12    (4)\r\n" );
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document.write( "     x + 2y +   4z =  27    (5)\r\n" );
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document.write( "    2x +  3y +  4z =  35    (6)\r\n" );
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document.write( "Add equations (4) and (5) and then subtract equation (6) from the sum.  You will get\r\n" );
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document.write( "                 z = 4.\r\n" );
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document.write( "Now substitute z= 4 into equations (4) and (5).  You will get\r\n" );
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document.write( "     x +  y +  4 = 12       (7)\r\n" );
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document.write( "     x + 2y + 16 = 27       (8)\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "     x +  y =  8            (9)\r\n" );
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document.write( "     x + 2y = 11            (10)\r\n" );
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document.write( "Finally, from equation (10) subtract equation (9).  You will get\r\n" );
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document.write( "         y  = 3.\r\n" );
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document.write( "ANSWER.  3 (three) 12-pencils packages were sold.\r\n" );
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