document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84858>Question 84858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have 7 bags of marbles. There are 200 marbles in total. Using the clues below, work out how many marbles are in each bag.\r<BR>\n" );
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document.write( "Bag 1 + Bag 2 = 57 marbles<BR>\n" );
document.write( "Bag 2 + Bag 3 = 83 marbles<BR>\n" );
document.write( "Bag 3 + Bag 4 = 71 marbles<BR>\n" );
document.write( "Bag 4 + Bag 5 = 43 marbles<BR>\n" );
document.write( "Bag 5 + Bag 6 = 66 marbles<BR>\n" );
document.write( "Bag 6 + Bag 7 = 43 marbles\r<BR>\n" );
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document.write( "Thank you so much for your help. I tried to figure this out but came to no avail. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61142 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=61142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets use these variables for each bag:<BR>\n" );
document.write( "Bag 1 = a<BR>\n" );
document.write( "Bag 2 = b<BR>\n" );
document.write( "Bag 3 = c<BR>\n" );
document.write( "Bag 4 = d<BR>\n" );
document.write( "Bag 5 = e<BR>\n" );
document.write( "Bag 6 = f<BR>\n" );
document.write( "Bag 7 = g\r<BR>\n" );
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document.write( "Now set up the following system of equations\r<BR>\n" );
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document.write( "a + b = 57 \r\n" );
document.write( "    b + c = 83 \r\n" );
document.write( "        c + d = 71 \r\n" );
document.write( "            d + e = 43\r\n" );
document.write( "                e + f = 66\r\n" );
document.write( "                    f + g = 43 \r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "Also since we know how many marbles there are total, we can use this equation:\r<BR>\n" );
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document.write( "a+b+c+d+e+f+g=200\r\n" );
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document.write( "Now subtract (a+b=57), (c+d=71), and (f+g=43) from a+b+c+d+e+f+g=200 to eliminate everything but one bag (in this case bag 5 which is denoted \"e\")\r<BR>\n" );
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document.write( "  a+b+c+d+e+f+g=200\r\n" );
document.write( "-(a+b          =57)\r\n" );
document.write( "-(    c+d      =71)\r\n" );
document.write( "-(          f+g=43)\r\n" );
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document.write( "          e    =29\r\n" );
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document.write( "So we know that bag 5 has 29 marbles\r<BR>\n" );
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document.write( "Now plug in e=29 to find f<BR>\n" );
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document.write( "Bag 6:\r\n" );
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document.write( "29 + f = 66\r\n" );
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document.write( "f = 37\r\n" );
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document.write( "So we know that bag 6 has 37 marbles\r<BR>\n" );
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document.write( "Now plug in f=37 to find g<BR>\n" );
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document.write( "Bag 7:\r\n" );
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document.write( "37 + g = 43\r\n" );
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document.write( "g = 6\r\n" );
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document.write( "So we know that bag 7 has 6 marbles\r<BR>\n" );
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document.write( "Now plug in e=29 to find d<BR>\n" );
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document.write( "Bag 4:\r\n" );
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document.write( "d + 29 = 43\r\n" );
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document.write( "d = 14\r\n" );
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document.write( "So we know that bag 4 has 14 marbles\r<BR>\n" );
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document.write( "Now plug in d=14 to find c<BR>\n" );
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document.write( "Bag 3:\r\n" );
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document.write( "c + 14 = 71\r\n" );
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document.write( "c = 57\r\n" );
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document.write( "So we know that bag 3 has 57 marbles\r<BR>\n" );
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document.write( "Now plug in c=57 to find b<BR>\n" );
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document.write( "Bag 2:\r\n" );
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document.write( "b + 57 = 83\r\n" );
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document.write( "b = 26\r\n" );
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document.write( "So we know that bag 2 has 26 marbles\r<BR>\n" );
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document.write( "Now plug in b=26 to find a<BR>\n" );
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document.write( "Bag 1:\r\n" );
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document.write( "a + 26 = 57\r\n" );
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document.write( "a = 31\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "So we know that bag 1 has 26 marbles\r<BR>\n" );
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document.write( "So here's a summary of all of the bags:\r<BR>\n" );
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document.write( "Bag 1 = 31 marbles<BR>\n" );
document.write( "Bag 2 = 26 marbles<BR>\n" );
document.write( "Bag 3 = 57 marbles<BR>\n" );
document.write( "Bag 4 = 14 marbles<BR>\n" );
document.write( "Bag 5 = 29 marbles<BR>\n" );
document.write( "Bag 6 = 37 marbles<BR>\n" );
document.write( "Bag 7 = 6 marbles\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "31+26+57+14+29+37+6=200<BR>\n" );
document.write( "200=200  </SPAN>\n" );
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