document.write( "Question 1169996: A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28. A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37. Find the cost per pound of the cinnamon tea and of the spice tea. \n" ); document.write( "

Algebra.Com's Answer #794869 by ikleyn(52909) $\"\"$ $\"About$

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A merchant mixed 12 lb of a cinnamon tea with 5 lb of spice tea. The 17-pound mixture cost $28.
\n" ); document.write( "A second mixture included 14 lb of the cinnamon tea and 8 lb of the spice tea. The 22-pound mixture cost $37.
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document.write( "    12x + 5y = 28   dollars     (1)\r\n" );
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document.write( "    14x + 8y = 37   dollars     (2)\r\n" );
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document.write( "Multiply equation (1) by 8 (both sides).\r\n" );
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document.write( "Multiply equation (2) by 5 (both sides).  You will get\r\n" );
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document.write( "    96x + 40y = 28*8            (3)\r\n" );
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document.write( "    70x + 40y = 37*5            (4)\r\n" );
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document.write( "From equation (3), subtract equation (4).  You will get\r\n" );
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document.write( "    26x       = 28*8 - 37*5 = 39\r\n" );
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document.write( "      x                     = 39/26 =  = 1.50  dollars.\r\n" );
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document.write( "To find y, substitute the found value x= 1.50 into equation (1). You will get\r\n" );
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document.write( "    12*1.50 + 5y = 28\r\n" );
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document.write( "    18      + 5y = 28\r\n" );
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document.write( "              5y = 28-18 = 10\r\n" );
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document.write( "               y         = 10/2 = 5.\r\n" );
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document.write( "ANSWER.  Cinamon tea price is $1.50 per pound.  The spice tea price is $2.00 dollars per pound.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The method I used in the solution, is called the ELIMINATION method.\r
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