document.write( "Question 53523: Mr. Smith has $100.00 to buy 100 animals with. Cows cost $10.00 each, pigs cost $3.00 each and chickent cost $.50 each. How many can he buy with exactly $100.00. \r
\n" ); document.write( "\n" ); document.write( "I have this equation so far, but where do I go from here?\r
\n" ); document.write( "\n" ); document.write( "10x + 3y + .5z = 100 \n" ); document.write( "

Algebra.Com's Answer #35759 by AnlytcPhil(1806) $\"\"$ $\"About$

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Mr. Smith has $100.00 to buy 100 \r\n" );
document.write( "animals with. Cows cost $10.00 each, \r\n" );
document.write( "pigs cost $3.00 each and chickens \r\n" );
document.write( "cost $.50 each. How many can he buy \r\n" );
document.write( "with exactly $100.00.  I have this \r\n" );
document.write( "equation so far, but where do I go \r\n" );
document.write( "from here? \r\n" );
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document.write( "10x + 3y + .5z = 100\r\n" );
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document.write( "Multiply through by 10 to clear decimal:\r\n" );
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document.write( "100x + 30y + 5z = 1000\r\n" );
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document.write( "Divide by 5\r\n" );
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document.write( "20x + 6y + z = 200\r\n" );
document.write( "   x + y + z = 100\r\n" );
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document.write( "19x + 5y = 100\r\n" );
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document.write( "19x = 100 - 5y\r\n" );
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document.write( "19x = 5(20 - y)\r\n" );
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document.write( "  x = 5(20 - y)/19\r\n" );
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document.write( "Since x is a positive integer,\r\n" );
document.write( "the 19 must divide evenly into\r\n" );
document.write( "5(20 - y).  the 19 will not\r\n" );
document.write( "divide evenly into the 5, so\r\n" );
document.write( "19 must divide into 20 - y.\r\n" );
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document.write( "20 - y is at most 19, since\r\n" );
document.write( "y must be at least 1.  The\r\n" );
document.write( "only integer at least 19\r\n" );
document.write( "which is divisible by 19 is\r\n" );
document.write( "19 itself.  Therefore\r\n" );
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document.write( "20 - y = 19\r\n" );
document.write( "    -y = -1\r\n" );
document.write( "     y = 1 \r\n" );
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document.write( "x = 5(20 - y)/19\r\n" );
document.write( "x = 5(20 - 1)/19\r\n" );
document.write( "x = 5(19)/19\r\n" );
document.write( "x = 5\r\n" );
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document.write( "x + y + z = 100\r\n" );
document.write( "5 + 1 + z = 100\r\n" );
document.write( "    6 + z = 100\r\n" );
document.write( "        z = 94\r\n" );
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document.write( "Therefore he bought\r\n" );
document.write( "5 cows, 1 pig, \r\n" );
document.write( "and 94 chickens.\r\n" );
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document.write( "Edwin

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