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\n" ); document.write( "First a typical standard algebraic solution....
\n" ); document.write( "p = # of pigs
\n" ); document.write( "c = # of chickens
\n" ); document.write( "Each pig has four feet and each chicken has two; each pig and each chicken has one head.
\n" ); document.write( "The total number of heads is 27:
\n" ); document.write( "p+c = 27 [1]
\n" ); document.write( "The total number of feet is 78:
\n" ); document.write( "4p+2c = 78 [2]
\n" ); document.write( "Solve the pair of equations [1] and [2] by your favorite method. When the two equations are in this form, elimination is my preference.
\n" ); document.write( "Multiply equation [1] by 2 and compare to equation [2] to eliminate c and solve for p.
\n" ); document.write( "2p+2c = 54
\n" ); document.write( "4p+2c = 78
\n" ); document.write( "2p = 78-54 = 24
\n" ); document.write( "p = 24/2 = 12
\n" ); document.write( "The number of pigs is 12, so the number of chickens is 27-12 = 15.
\n" ); document.write( "ANSWER: 12 pigs, 15 chickens
\n" ); document.write( "And now an informal solution, done mentally and quickly.
\n" ); document.write( "If all 27 animals were chickens, the number of feet would be 27*2 = 54.
\n" ); document.write( "The actual number of feet is 78, which is 24 more than that.
\n" ); document.write( "Each pig has 2 more feet than each chicken, so the number of pigs is 24/2 = 12.
\n" ); document.write( "ANSWER: 12 pigs and 17-12 = 15 chickens
\n" ); document.write( "For studying math, understanding the formal algebraic solution is important.
\n" ); document.write( "But solving problems like this informally using logical reasoning is excellent brain exercise.
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