document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019851>Question 1019851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Martians have two heads and five legs. There was a \"meet and greet\" party that had both Martians and Earthlings. At that party I counted 29 heads and 67 legs. How many Martians and Earthlings were at the party? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635782 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of martians.<BR>\n" );
document.write( "let y equal the number of earthlings.\r<BR>\n" );
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document.write( "each martian has 2 heads and 5 legs.<BR>\n" );
document.write( "each earthling 1 head and 2 legs.\r<BR>\n" );
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document.write( "you have counted 29 heads and 67 legs at the party.\r<BR>\n" );
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document.write( "since each martian has 2 heads, then the number of martian heads at the party is equal to 2x.\r<BR>\n" );
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document.write( "since each earthling has 1 head, then the number of earthling heads at the party is equal to y.\r<BR>\n" );
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document.write( "you get 2x + y = 29\r<BR>\n" );
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document.write( "since each martian has 5 legs, then the number of martian legs at the party is equal to 5x.\r<BR>\n" );
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document.write( "since each earthling has 2 legs, then the number of earthling legs at the party is equal to 2y.\r<BR>\n" );
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document.write( "you get 5x + 2y = 67\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "2x + y = 29<BR>\n" );
document.write( "5x + 2y = 67\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is and you get:\r<BR>\n" );
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document.write( "4x + 2y = 58<BR>\n" );
document.write( "5x + 2y = 67\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "x = 9\r<BR>\n" );
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document.write( "when x = 9, 4x + 2y = 58 becomes 36 + 2y = 58<BR>\n" );
document.write( "solve for y to get y = (58 - 36) / 2 = 22/2 = 11\r<BR>\n" );
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document.write( "you have x = 9 and y = 11.\r<BR>\n" );
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document.write( "there were 9 martians and 11 earthlings at the party.\r<BR>\n" );
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document.write( "9 martians give you 2*9 = 18 heads and 5*9 = 45 legs<BR>\n" );
document.write( "11 earthlings gives you 1*11 = 11 heads and 2*11 = 22 legs\r<BR>\n" );
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document.write( "total heads = 11 + 18 = 29<BR>\n" );
document.write( "total legs = 45 + 22 = 67\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "solution is:\r<BR>\n" );
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document.write( "there were 9 martians and 11 earthlings at the party.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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