document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127546>Question 127546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this problem for an hour now and I just don't get it. I would really appreciate some help.\r<BR>\n" );
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document.write( "One lemon costs one fils.<BR>\n" );
document.write( "One orange costs twenty fils.<BR>\n" );
document.write( "One apple costs fifty fils.\r<BR>\n" );
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document.write( "You need to buy a total for 100 fruits and 1 Kuwait Dinar (1000 fils in total) How many of each fruit will you buy?\r<BR>\n" );
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document.write( "Thanks a lot! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93497 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Number of lemons: l<BR>\n" );
document.write( "Number of oranges: o<BR>\n" );
document.write( "Number of apples: a\r<BR>\n" );
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document.write( "You need to buy 100 pieces of fruit, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+o+%2B+a=100 ALIGN=MIDDLE  ALT=\"l+%2B+o+%2B+a=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The value of the lemons you buy, since they cost 1 fil each, is just l.<BR>\n" );
document.write( "The value of the oranges is 20o<BR>\n" );
document.write( "The value of the apples is 50a\r<BR>\n" );
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document.write( "The total value must be 1000 fils.\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+20o+%2B+50a+=+1000 ALIGN=MIDDLE  ALT=\"l+%2B+20o+%2B+50a+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But now you are stuck because you don't have any other information.  You have three unknown quantities, but only two equations.  However, you actually do have more information, it is just hidden a bit.\r<BR>\n" );
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document.write( "Since apples cost 50 fils, the most you could buy would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F50+=+20 ALIGN=MIDDLE  ALT=\"1000%2F50+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but then you would only have 20 pieces of fruit and no money to buy anything else.  So we know the answer must have a value for apples that is a good deal less than 20.\r<BR>\n" );
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document.write( "Let's see what happens if we buy no apples at all:\r<BR>\n" );
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document.write( "From our original set of equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+o=100-a ALIGN=MIDDLE  ALT=\"l+%2B+o=100-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+20o+=+1000-50a ALIGN=MIDDLE  ALT=\"l+%2B+20o+=+1000-50a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Case: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+o=100 ALIGN=MIDDLE  ALT=\"l+%2B+o=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+20o+=+1000 ALIGN=MIDDLE  ALT=\"l+%2B+20o+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the first equation by -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-l-o=-100 ALIGN=MIDDLE  ALT=\"-l-o=-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add it to the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19o=900 ALIGN=MIDDLE  ALT=\"19o=900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=o=47.36842 ALIGN=MIDDLE  ALT=\"o=47.36842\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you can't buy a fractional part of an orange, this answer can be excluded.\r<BR>\n" );
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document.write( "Let's divide and conquer:\r<BR>\n" );
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document.write( "Case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10 ALIGN=MIDDLE  ALT=\"a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+o=100-10 ALIGN=MIDDLE  ALT=\"l+%2B+o=100-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+20o+=+1000-500 ALIGN=MIDDLE  ALT=\"l+%2B+20o+=+1000-500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by -1 again:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-l-o=-90 ALIGN=MIDDLE  ALT=\"-l-o=-90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%2B20o=500 ALIGN=MIDDLE  ALT=\"l%2B20o=500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19o=410 ALIGN=MIDDLE  ALT=\"19o=410\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we get another fractional result.  Hmmm.  What are the possibilities?\r<BR>\n" );
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document.write( "If you take all the possibilities for the number of apples purchased,  19 times the number of oranges must be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281000-50a%29-%28100-a%29=900-49a ALIGN=MIDDLE  ALT=\"%281000-50a%29-%28100-a%29=900-49a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So for all possible values of a, and we know that a > 0 and a < 20, what are the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900-49a ALIGN=MIDDLE  ALT=\"900-49a\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "Here's a list from a = 1 to a = 18.\r<BR>\n" );
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document.write( "851<BR>\n" );
document.write( "802<BR>\n" );
document.write( "753<BR>\n" );
document.write( "704<BR>\n" );
document.write( "655<BR>\n" );
document.write( "606<BR>\n" );
document.write( "557<BR>\n" );
document.write( "508<BR>\n" );
document.write( "459<BR>\n" );
document.write( "410<BR>\n" );
document.write( "361<BR>\n" );
document.write( "312<BR>\n" );
document.write( "263<BR>\n" );
document.write( "214<BR>\n" );
document.write( "165<BR>\n" );
document.write( "116<BR>\n" );
document.write( "67<BR>\n" );
document.write( "18\r<BR>\n" );
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document.write( "The question becomes which of these numbers is evenly divisible by 19?\r<BR>\n" );
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document.write( "I'll save you a little calculator work:  it is 361, which equates to a = 11.\r<BR>\n" );
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document.write( "Case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=11 ALIGN=MIDDLE  ALT=\"a=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+o=100-11 ALIGN=MIDDLE  ALT=\"l+%2B+o=100-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l+%2B+20o+=+1000-550 ALIGN=MIDDLE  ALT=\"l+%2B+20o+=+1000-550\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by -1 again:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-l-o=-89 ALIGN=MIDDLE  ALT=\"-l-o=-89\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%2B20o=450 ALIGN=MIDDLE  ALT=\"l%2B20o=450\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19o=361 ALIGN=MIDDLE  ALT=\"19o=361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=o=19 ALIGN=MIDDLE  ALT=\"o=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have 11 apples, 19 oranges, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-11-19=70 ALIGN=MIDDLE  ALT=\"100-11-19=70\"   DISABLED_style= \"max-width:90%; height:auto;\" > lemons.\r<BR>\n" );
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document.write( "Check:  11 apples @ 50 = 550, 19 oranges @ 20 = 380, and 70 lemons @ 1 = 70\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=550+%2B+380+%2B+70+=+1000 ALIGN=MIDDLE  ALT=\"550+%2B+380+%2B+70+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+%2B+19+%2B+70+=+100 ALIGN=MIDDLE  ALT=\"11+%2B+19+%2B+70+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer checks. </SPAN>\n" );
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