document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335123>Question 335123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cory has 3000 bananas.   Cory has a camel that can carry 1000 bananas at a time.  Cory's camel eats 1 banana every mile he travels.  How many bananas can Cory get to the market?    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240171 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=240171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:\r<BR>\n" );
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document.write( "Cory has 3000 bananas.<BR>\n" );
document.write( "Cory has a camel that can carry 1000 bananas at a time.<BR>\n" );
document.write( "Cory's camel eats 1 banana for every mile the camel travels.\r<BR>\n" );
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document.write( "Assumption:\r<BR>\n" );
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document.write( "The camel has to get to market and the camel has to get back from market.\r<BR>\n" );
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document.write( "Analysis.\r<BR>\n" );
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document.write( "The camel consumes 1 banana for every mile the camel travels.\r<BR>\n" );
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document.write( "The distance is x miles (unknown at this time).\r<BR>\n" );
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document.write( "the camel will have to make 3 trips because there are 3000 bananas and the<BR>\n" );
document.write( "camel can only carry 1000 bananas each trip.\r<BR>\n" );
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document.write( "Each trip the camel travels x miles to get to the market and x miles to get<BR>\n" );
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document.write( "That means that each trip, the camel travels 2 * x miles.\r<BR>\n" );
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document.write( "For 3 trips, that means the camel travels 3 * (2 * x) = 6 * x miles.\r<BR>\n" );
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document.write( "Since the camel consumes 1 banana for every mile that the camel travels,<BR>\n" );
document.write( "this means that the camel will consume 6 * x bananas in total.\r<BR>\n" );
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document.write( "What can be sold at market are the bananas that the camel has not consumed.\r<BR>\n" );
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document.write( "Since there are 3000 bananas in total, and the camel will have to travel 6 *<BR>\n" );
document.write( "x miles in total, then the number of bananas that can be sold at market is:\r<BR>\n" );
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document.write( "3000 - 6*x\r<BR>\n" );
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document.write( "If the distance to market is 100 miles, this means that 3000 - 600 = 2400<BR>\n" );
document.write( "bananas can be sold as market.\r<BR>\n" );
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document.write( "This works out as follows:\r<BR>\n" );
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document.write( "First trip:\r<BR>\n" );
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document.write( "Camel gets loaded with 1000 bananas.<BR>\n" );
document.write( "Camel consumes 100 bananas to get to market.<BR>\n" );
document.write( "There are 900 bananas left.<BR>\n" );
document.write( "Camel needs an additional 100 bananas to get back home.<BR>\n" );
document.write( "There are 800 bananas left that can be sold.\r<BR>\n" );
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document.write( "This happens 3 times.\r<BR>\n" );
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document.write( "Total number of bananas that can be sold is 3 * 800 = 2400.\r<BR>\n" );
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document.write( "A major assumption is that the camel has to get to market and back and that<BR>\n" );
document.write( "the camel eats 100 bananas every mile.\r<BR>\n" );
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document.write( "Change this assumption and the answer changes.\r<BR>\n" );
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document.write( "Before we change this assumption, let's assume the distance is 1000 miles.\r<BR>\n" );
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document.write( "what happens then?\r<BR>\n" );
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document.write( "the formula states that the number of bananas that can be sold at market is<BR>\n" );
document.write( "given by the equation 3000 - 6*x.\r<BR>\n" );
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document.write( "If x equals 1000, then it is clear that there are not enough bananas because<BR>\n" );
document.write( "3000 - 6000 = -3000.\r<BR>\n" );
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document.write( "The maximum distance would be 500 miles and no bananas would be left to<BR>\n" );
document.write( "sell, because 3000 - 500*6 = 3000 - 3000 = 0.\r<BR>\n" );
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document.write( "Now let's change the assumption.\r<BR>\n" );
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document.write( "Let's assume that the camel eats 1 banana each mile that the camel takes to<BR>\n" );
document.write( "get to market, but that on the return trip the camel eats something else,<BR>\n" );
document.write( "just not bananas.\r<BR>\n" );
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document.write( "The formula then becomes:\r<BR>\n" );
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document.write( "Number of bananas that can be sold at market is 3000 - 3 * x.\r<BR>\n" );
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document.write( "That's 3 trips to market at x miles each trip.\r<BR>\n" );
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document.write( "Now assume that the distance is 100 miles.\r<BR>\n" );
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document.write( "You get 3000 - 3*100 = 3000 - 300 = 2700 bananas that can be sold at market.\r<BR>\n" );
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document.write( "If the distance is 500 miles, you get 3000 - 3 * 500 = 3000 - 1500 = 1500<BR>\n" );
document.write( "bananas that can be sold at market.\r<BR>\n" );
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document.write( "If the distance is 1000 miles, you get 3000 - 3 * 1000 = 0 bananas that can<BR>\n" );
document.write( "be sold at market.\r<BR>\n" );
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document.write( "The camel has ate them all.\r<BR>\n" );
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document.write( "At 1000 miles, under the assumption that the camel only consumes 1 banana<BR>\n" );
document.write( "each mile getting to market, and consumes no bananas on the return trip from<BR>\n" );
document.write( "market, you get:\r<BR>\n" );
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document.write( "First trip:\r<BR>\n" );
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document.write( "Camel is loaded with 1000 bananas.<BR>\n" );
document.write( "Camel eats 1 banana for every mile camel travels to market.<BR>\n" );
document.write( "After 1000 miles, camel has consumed 1000 bananas.<BR>\n" );
document.write( "There are no bananas left to sell at market.\r<BR>\n" );
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document.write( "This happens for each of 3 trips, assuming the banana seller is dumb enough<BR>\n" );
document.write( "to make the additional 2 trips after finding out that he has no bananas to<BR>\n" );
document.write( "sell.\r<BR>\n" );
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document.write( "I suspect the problem makes the second assumption.\r<BR>\n" );
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document.write( "That is that the camel consumes 1 banana for each mile of travel going to<BR>\n" );
document.write( "market only.\r<BR>\n" );
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document.write( "The answer, under that assumption, is that 0 bananas can be sold at market<BR>\n" );
document.write( "because the camel has consumed them all, assuming the distance is 1000 miles.<BR>\n" );
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