document.write( "Question 1190210: A merchant wishes to mix gourmet coffee selling for $8 per pound, $10 per pound, and $15 per pound to get 50 pounds of a mixture that can be sold for $11.70 per pound. The amount of the $8 coffee must be 3 pounds more than the amount of the $10 coffee. Find the number of pounds of each that must be used \n" ); document.write( "

Algebra.Com's Answer #821809 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "A merchant wishes to mix gourmet coffee selling for $8 per pound, $10 per pound,
\n" ); document.write( "and $15 per pound to get 50 pounds of a mixture that can be sold for $11.70 per pound.
\n" ); document.write( "The amount of the $8 coffee must be 3 pounds more than the amount of the $10 coffee.
\n" ); document.write( "Find the number of pounds of each that must be used.
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document.write( "Let x be the pounds of the $10 coffee;\r\n" );
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document.write( "then $8 coffee is (x+3) pounds, and the $15 coffee is the rest (50-x-(x+3)) = (47-2x) pounds.\r\n" );
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document.write( "The combined cost of ingredients and the cost of the mixture is the same, \r\n" );
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document.write( "so we write this equation\r\n" );
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document.write( "    10x + 8(x+3) + 15(47-2x) = 50*11.70.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    10x + 8x + 24 + 15*47 - 30x = 50*11.70\r\n" );
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document.write( "          -12x = 50*11.70 - 24 - 15*27\r\n" );
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document.write( "          -12x = -144\r\n" );
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document.write( "             x = (-144) / (-12) = 12.\r\n" );
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document.write( "ANSWER.  12 pounds of the $10 coffee;  12+3 = 15 pound of the $8 pounds coffee and the rest, 50-12-15 = 23 pounds of the $15 coffee.\r\n" );
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document.write( "CHECK.   = 11.70 dollars per pound, the averaged price.  ! Precisely correct !\r\n" );
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