document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127831>Question 127831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this math problem.  Tarzan gave Jane a 1 pound box of chocolates.  He knows that when they share a 1 pound box of chocolate it usually lasts for 2 weeks.  When he eats a 1 pound box of chocolate, it lasts for 6 weeks.  Based on this information, how long should it take Jane to eat a 1 pound box of chocolate by herself.\r<BR>\n" );
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document.write( "Any help would be appreciated!  Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93622 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=93622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When Tarzan eats a 1 lb box of chocolates, the box lasts for 6 weeks. Therefore, Tarzan's rate<BR>\n" );
document.write( "of eating chocolate is 1/6 lb per week. This means that when he and Jane eat a box together in<BR>\n" );
document.write( "two weeks, that he eats 1/6 box each week and in the two weeks he eats 2/6 of a box. And <BR>\n" );
document.write( "2/6 reduces to 1/3. So in the two weeks that he and Jane polish off the chocolates, he<BR>\n" );
document.write( "eats 1/3 of the box and Jane eats the other 2/3.<BR>\n" );
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document.write( "Since Jane eats 2/3 of a box in 2 weeks, that means that each week she eats 1/3 of a box.<BR>\n" );
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document.write( "From this you can tell that to eat a box by herself at 1/3 a box per week. It will take Jane <BR>\n" );
document.write( "(a true choco-holic) 3 weeks to finish a box.<BR>\n" );
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document.write( "That's the thought process to get the answer. To do it from the math process, you can<BR>\n" );
document.write( "start by letting T represent Tarzan's rate of eating chocolate and J represent Jane's rate of<BR>\n" );
document.write( "eating chocolate. When they work together they eat one (1) box of chocolates in 2 weeks.<BR>\n" );
document.write( "The amount of chocolate each eats is determined by multiplying their rate of eating by the<BR>\n" );
document.write( "time they eat, the time they eat being 2 weeks. In other words Tarzan eats T*2 and Jane <BR>\n" );
document.write( "eats J*2 and this totals to 1 box. In equation form this is:<BR>\n" );
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document.write( "T*2 + J*2 = 1<BR>\n" );
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document.write( "But Tarzan's rate T comes from the fact that in 6 weeks at the rate he eats he finishes<BR>\n" );
document.write( "one box. In equation form this is:<BR>\n" );
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document.write( "T*6 = 1<BR>\n" );
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document.write( "Solve for T by dividing both sides by 6 and you get:<BR>\n" );
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document.write( "T = 1/6<BR>\n" );
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document.write( "Substitute this value for T into the equation we wrote for Tarzan and Jane working <BR>\n" );
document.write( "together and you convert:<BR>\n" );
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document.write( "T*2 + J*2 = 1<BR>\n" );
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document.write( "into:<BR>\n" );
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document.write( "(1/6)*2 + J*2 = 1<BR>\n" );
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document.write( "Multiply out the first term and you get:<BR>\n" );
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document.write( "2/6 + J*2 = 1<BR>\n" );
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document.write( "Get rid of the denominator by multiplying both sides (all terms on both sides) by 6. When you<BR>\n" );
document.write( "do that multiplication of every term by 6 you get:<BR>\n" );
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document.write( "2 + J*12 = 6<BR>\n" );
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document.write( "Get rid of the 2 on the left side by subtracting 2 from both sides and you have:<BR>\n" );
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document.write( "J*12 = 4<BR>\n" );
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document.write( "Solve for J by dividing both sides by 12 to get:<BR>\n" );
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document.write( "J = 4/12 = 1/3<BR>\n" );
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document.write( "Now you can write the equation that says Jane's rate times W weeks equals 1 box of chocolate<BR>\n" );
document.write( "by herself. In equation form this is:<BR>\n" );
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document.write( "J*W = 1<BR>\n" );
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document.write( "Substitute 1/3 for J and this equation becomes:<BR>\n" );
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document.write( "(1/3)*W = 1<BR>\n" );
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document.write( "Get rid of the denominator by multiplying both sides of this equation (all terms) by 3<BR>\n" );
document.write( "and the result is:<BR>\n" );
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document.write( "W = 3<BR>\n" );
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document.write( "Jane eats a box of chocolates by herself in 3 weeks.<BR>\n" );
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document.write( "Sometimes the math method of solving is confusing and if you really stop focusing on the<BR>\n" );
document.write( "need to find an equation, you can think your way through the problem just as we did way<BR>\n" );
document.write( "back at the beginning.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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