document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131973>Question 131973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96410 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let P represent the number of pigs and C represent the number of chickens. <BR>\n" );
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document.write( "Since each type of animal has 1 head and there are 27 heads, then the number of pigs plus the<BR>\n" );
document.write( "number of chickens must total 27. In equation form this is:<BR>\n" );
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document.write( "P + C = 27<BR>\n" );
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document.write( "And since the number of pigs legs is 4 times the number of pigs (i.e., 4P) and the number of <BR>\n" );
document.write( "chicken legs is 2 times the number of chickens (2C), then the total number of legs is 4P + 2C.<BR>\n" );
document.write( "But you are told that this number is 78. So we can write the equation:<BR>\n" );
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document.write( "4P + 2C = 78<BR>\n" );
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document.write( "From the first equation for the number of heads, we can solve for P by subtracting C <BR>\n" );
document.write( "from both sides to get:<BR>\n" );
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document.write( "P = 27 - C<BR>\n" );
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document.write( "Since P = 27 - C we can substitute 27 - C for P in the second equation ... the equation for<BR>\n" );
document.write( "the number of legs. Replacing P by 27 - C in this equation results in:<BR>\n" );
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document.write( "4(27 - C) + 2C = 78<BR>\n" );
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document.write( "Multiply out the left side by multiplying 4 times each of the terms in the parentheses and<BR>\n" );
document.write( "the equation becomes:<BR>\n" );
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document.write( "108 - 4C + 2C = 78<BR>\n" );
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document.write( "On the left side when we combine the two terms that contain C we get:<BR>\n" );
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document.write( "108 - 2C = 78<BR>\n" );
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document.write( "Get rid of the 108 on the left side by subtracting 108 from both sides and you get:<BR>\n" );
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document.write( "-2C = -30<BR>\n" );
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document.write( "Solve for C by dividing both sides by -2 and we get:<BR>\n" );
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document.write( "C = -30/-2 = 15<BR>\n" );
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document.write( "There are 15 chickens. Since there is a total of 27 heads, the number of pigs must be <BR>\n" );
document.write( "27 minus 15 = 12 pigs.<BR>\n" );
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document.write( "Just as another check, the 12 pigs have a total of 4*12 = 48 legs and the 15 chickens have<BR>\n" );
document.write( "a total of 15*2 = 30 legs. So the total number of legs is 48 + 30 = 78 ... just as the problem<BR>\n" );
document.write( "says it should be. So our answers check ... there are 12 pigs and 15 chickens.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and shows you a way of working it through to<BR>\n" );
document.write( "an answer.<BR>\n" );
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