document.write( "Question 421223: You must buy 100 chickens for exactly $100. You must buy at least one chicken from each store. The first store charges 5 cents/chicken, the second charges $1/chicken and the third charges $5/chicken. How many chickens should you buy from each store? I know the answer is 80 for .05, 19 for $1, and 1 for$5. Is there any mathematical equation you can apply to solve it though, because I just used guess and check. \n" ); document.write( "
Algebra.Com's Answer #294190 by Edwin McCravy(20060)\"\" \"About 
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document.write( "You must buy 100 chickens for exactly $100. You must buy at least one chicken\r\n" );
document.write( "from each store. The first store charges 5 cents/chicken, the second charges\r\n" );
document.write( "$1/chicken and the third charges $5/chicken. How many chickens should you buy\r\n" );
document.write( "from each store?  I know the answer is 80 for .05, 19 for $1, and 1 for$5.  Is\r\n" );
document.write( "there any mathematical equation you can apply to solve it though, because I\r\n" );
document.write( "just used guess and check. \r\n" );
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document.write( "You have the number of chickens for $1 and 5$ reversed.\r\n" );
document.write( "The answer is 80 for .05, 1 for $1, and 19 for $5.\r\n" );
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document.write( "Yes it can be done by algebra, since we know that the \r\n" );
document.write( "solutions must be in positive integers.  \r\n" );
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document.write( "Let x = the number of chickens at  $.05 each\r\n" );
document.write( "Let y = the number of chickens at $1.00 each\r\n" );
document.write( "Let z = the number of chickens at $5.00 each\r\n" );
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document.write( "The system is\r\n" );
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document.write( ".05x + 1.00y + 5.00z = 100\r\n" );
document.write( "           x + y + z = 100\r\n" );
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document.write( "Since both left sides equal to 100, they are equal to \r\n" );
document.write( "each other. Setting those equal:\r\n" );
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document.write( ".05x + 1.00y + 5.00z = x + y + z\r\n" );
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document.write( "                  4z = .95x\r\n" );
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document.write( "Multiplying both sides by 100\r\n" );
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document.write( "                400z = 95x\r\n" );
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document.write( "Dividing both sides by 5\r\n" );
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document.write( "                 80z = 19x\r\n" );
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document.write( "Divide through by 80x\r\n" );
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document.write( "                 z/x = 19/80\r\n" );
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document.write( "So the fraction z/x must be the same as or it must reduce to 19/80.\r\n" );
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document.write( "So let z = 19n and x = 80n where n is a positive integer, since only\r\n" );
document.write( "fractions of the form (19n)/(80n) will be the same as or reduce to 19/80.\r\n" );
document.write( "Substitute those in:\r\n" );
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document.write( "    x + y + z = 100\r\n" );
document.write( "80n + y + 19n = 100\r\n" );
document.write( "      99n + y = 100\r\n" );
document.write( "            y = 100 - 99n\r\n" );
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document.write( "Since y must be positive, n can only be 1. So\r\n" );
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document.write( "            y = 100 - 99(1)\r\n" );
document.write( "            y = 1\r\n" );
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document.write( "   z = 19n  and x = 80n \r\n" );
document.write( "   z = 19*1 and x = 80*n         \r\n" );
document.write( "   z = 19   and x = 80   \r\n" );
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document.write( "Edwin
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