document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9355>Question 9355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> supose 5 bales of hay are weighed 2 at a time in all possible ways. the weights in pounds are 110,112,113,114,114,116,117,118,120,and 121.  how much  does each bale weigh? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5112 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=5112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  First of all,you did two mistakes <BR>\n" );
document.write( "  1) wrong category of posting<BR>\n" );
document.write( "  2) the numbers are 110,112,113,114,115,116,117,118,120,and 121 <BR>\n" );
document.write( "    [No two 114s, one should be 115. otherwise no legal soutions] \r<BR>\n" );
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document.write( " Consider a pentagon , each vertex can be connected to four of the <BR>\n" );
document.write( " other vertices. Hence, the summation of the 10 numbers should be <BR>\n" );
document.write( " equal to 4 times the sum of the five bales.<BR>\n" );
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document.write( " Since the total of these 10 numbers is 1156, the sum of the 5 balse is <BR>\n" );
document.write( " 1156/4 = 289 [use Excel]<BR>\n" );
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document.write( " Let the five bales be A,B,C,D and E (in this order, ie A is the lightest,<BR>\n" );
document.write( " E is the heaviest) <BR>\n" );
document.write( " Clearly ,we know that A + B = 110 & D+E = 121.\r<BR>\n" );
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document.write( " So,we get the middle one C = 289 - 110 - 121 = 58,<BR>\n" );
document.write( " and the 2nd number 112 in the listing should be A + C, <BR>\n" );
document.write( " hence A = 112 - 58 = 54, and so B = 110 - 54 = 56.<BR>\n" );
document.write( " whence, 120 should be C + E, and we obtain E = 120 - 58 = 62.<BR>\n" );
document.write( " Finally, D = 121 - 62 = 59.<BR>\n" );
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document.write( " Now we get the weights are 54,56,58, 59 & 62 pounds.\r<BR>\n" );
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document.write( " Of course, you can set up a system of 10 linear equations in 5 variables<BR>\n" );
document.write( " to solve this problem. But, the way above should be much faster.\r<BR>\n" );
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document.write( " Or you try to draw a pentagon to help you to understand. \r<BR>\n" );
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document.write( " Also, you have to check correctness of the answer.<BR>\n" );
document.write( " That is, these 5 numbers do make the given listing.\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
document.write( "  \r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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