document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177099>Question 1177099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two kinds of fruits are displayed in a fruit stand. One is avocado fruit whose number is no more than thrice the other, which is melon. How many avocado and melons are there if there are atleast 20 total of fruits displayed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837736 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52873)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Two kinds of fruits are displayed in a fruit stand. <BR>\n" );
document.write( "One is avocado fruit whose number is no more than thrice the other, <BR>\n" );
document.write( "which is melon. How many avocado and melons are there <BR>\n" );
document.write( "if there are at least 20 total of fruits displayed.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;@mananth incorrectly interprets the problems restrictions;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;THEREFORE, &nbsp;his answer, &nbsp;his solution and his teaching &nbsp;ALL &nbsp;are &nbsp;WRONG.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;I came to bring you a correct solution and to teach you in a right way.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let x be the number of melons, and\r\n" );
document.write( "let y be the number of avocados.\r\n" );
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document.write( "From the condition, you have these inequalities\r\n" );
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document.write( "    y <= 3x        (1)   (the number of avocados is no more than thrice the melons)\r\n" );
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document.write( "    x + y >= 20    (2)   (there are at least 20 total fruits displayed)\r\n" );
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document.write( "Make a plot of the lines \r\n" );
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document.write( "    y = 3x         (3)\r\n" );
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document.write( "    x + y = 20     (4)\r\n" );
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document.write( "These plots are shown below\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C+600%2C+-4%2C+26%2C+-4%2C+26%2C%0D%0A++++++++++++grid%281%29%2C%0D%0A%0D%0A+++++++graph++%28600%2C+600%2C+-4%2C+26%2C+-4%2C+26%2C++++++++%0D%0A++++++++++++++3x%2C+20-x%29%2C%0D%0A+++locate%2812%2C+++18%2C+++the%29%2C%0D%0A+++locate%2812%2C+++15%2C+solution%29%2C%0D%0A+++locate%2812%2C+++12%2C+++domain%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "       Plot  y = 3x (red),  y = 20-x (green)\r\n" );
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document.write( "The domain which is interesting to you is the part of the 1st quadrant, where x >= 0, y >= 0,\r\n" );
document.write( "which lies under the red line, but above the green line.\r\n" );
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document.write( "The integer points of the quadratic grid represent possible numbers \r\n" );
document.write( "of fruits. For example, these pairs are possible\r\n" );
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document.write( "    (x,y) = (melons,avocado) = (5,15), (6,15), (7,15), . . . (horizontal line in the plot y= 15)\r\n" );
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document.write( "                             = (6,18), (7,18), (8,18), . . . (horizontal line in the plot y= 18)\r\n" );
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document.write( "                             = (8,12), (8,13), (8,14), . . . , (8,24) (vertical   line in the plot x = 8)\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "So, your problem is reduced to the system of inequalities,<BR>\n" );
document.write( "and you can solve this system GRAPHICALLY to get better understanding of the solution set.\r<BR>\n" );
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document.write( "Again, &nbsp;note the @mananth incorrectly interpret the problems restrictions;<BR>\n" );
document.write( "THEREFORE, &nbsp;his answer, &nbsp;his solution and his teaching &nbsp;ALL &nbsp;are &nbsp;WRONG.\r<BR>\n" );
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document.write( "So, &nbsp;you better &nbsp;IGNORE &nbsp;his post for your safety.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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