document.write( "Question 1190209: The manager of the Sweet Candy Shop wishes to mix candy worth $4 per pound, $6 per pound, and $10 per pound to get 100 pounds of a mixture worth $7.60 per pound. The amount of $10 candy must equal the total amounts of the $4 and the $6 candy. How many pounds of each must be used? \n" ); document.write( "

Algebra.Com's Answer #821804 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The manager of the Sweet Candy Shop wishes to mix candy worth $4 per pound, $6 per pound, and $10 per pound
\n" ); document.write( "to get 100 pounds of a mixture worth $7.60 per pound. The amount of $10 candy must equal the total amounts
\n" ); document.write( "of the $4 and the $6 candy. How many pounds of each must be used?
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document.write( "As you read the condition, you understand that the amount of the $10 candy is exactly half of the total 100 pounds, \r\n" );
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document.write( "i.e. exactly 50 pounds, as well as the combined amount of the $4 and $6 candies is exactly the other half \r\n" );
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document.write( "of 100 pounds, i.e. 50 pounds.\r\n" );
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document.write( "So, regarding $10 candies, you just know the answer: it is 50 pounds.\r\n" );
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document.write( "To solve for the rest candies, let's assume that the anount of the $6 candies is x pounds;\r\n" );
document.write( "then the amount of the $4 candies is (50-x) pounds.\r\n" );
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document.write( "Then the cost of the mixture is  6x + 4*(50-x) + 50*10  dollars.\r\n" );
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document.write( "We want it would be 7.60*100 dollars.  So, we write the total cost equation\r\n" );
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document.write( "    6x + 4*(50-x) + 50*10 = 7.60*100.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    6x + 200 - 4x + 500 = 760\r\n" );
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document.write( "    6x - 4x = 760 - 500 - 200.\r\n" );
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document.write( "       2x   =       60\r\n" );
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document.write( "        x   =       60/2 = 30.\r\n" );
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document.write( "ANSWER.  Use 30 pounds of the $6 candy;  50-30 = 20 pounds of the $4 candy and 50 pounds of the $10 candy.\r\n" );
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document.write( "CHECK.  The average cost is   = 7.60 dollars per pound.  ! Precisely correct !\r\n" );
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