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Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.
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\n" ); document.write( "Let x = no. of cows
\n" ); document.write( "Let y = no. of pigs
\n" ); document.write( "Let z = no. of chicks
\n" ); document.write( ":
\n" ); document.write( "The no. of animal equation:
\n" ); document.write( "x + y + z = 100
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\n" ); document.write( "The cost of animals equation
\n" ); document.write( "10x + 3y + .5z = 100
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\n" ); document.write( "Multiply above equation by 2 and subtract the 1st equation:
\n" ); document.write( "20x + 6y + 1z = 200
\n" ); document.write( " x + y + z = 100
\n" ); document.write( "----------------------subtracting eliminates z
\n" ); document.write( " 19x + 5y = 100
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\n" ); document.write( "We know that x and y are integers; 19x and 5y have to be multiples of 5:
\n" ); document.write( "That leaves the only value we can have for x is 5
\n" ); document.write( ":
\n" ); document.write( "5 cows
\n" ); document.write( ":
\n" ); document.write( "19(5) + 5y = 100
\n" ); document.write( "95 + 5y = 100
\n" ); document.write( "5y = 100-95
\n" ); document.write( "5y = 5
\n" ); document.write( "y = one lonesome pig
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\n" ); document.write( "5 cows and 1 pig would leave us with 94 chickens
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\n" ); document.write( "Check our solutions in the cost equation
\n" ); document.write( "10(5) + 3(1) + .5(94) =
\n" ); document.write( "50.00 + 3.00 = 47.00 = $100\r
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