document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013111>Question 1013111</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An ice cream parlor made $200. They sold cups for $0.60, and cones for $2. How much cups of ice cream did they sell, and how many cones of ice cream did they sell?\r<BR>\n" );
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document.write( "I tried dividing $200 by $0.60, but what about the cones? \r<BR>\n" );
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document.write( "PLEASE EXPLAIN STEPS </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629289 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of cups sold<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of cones sold<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6x ALIGN=MIDDLE  ALT=\"0.6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= money (in $) made by selling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cups<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y ALIGN=MIDDLE  ALT=\"2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= money (in $) made by selling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > cones<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6x%2B2y=200 ALIGN=MIDDLE  ALT=\"0.6x%2B2y=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >= total money (in $) made by selling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cups and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > cones.<BR>\n" );
document.write( "I would expect another piece of information, such as the fact that they served a certain number of customers.<BR>\n" );
document.write( " <BR>\n" );
document.write( "IF the problem stated that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=135 ALIGN=MIDDLE  ALT=\"135\"   DISABLED_style= \"max-width:90%; height:auto;\" > servings (between cones and cups) were sold<BR>\n" );
document.write( "we would write that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=135 ALIGN=MIDDLE  ALT=\"x%2By=135\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and we would find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "by solving the system of linear equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=135%2C0.6x%2B2y=200%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=135%2C0.6x%2B2y=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=135%2C0.6x%2B2y=200%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=135%2C0.6x%2B2y=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2C0.6x%2B2y=200%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2C0.6x%2B2y=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2C0.6x%2B2%28135-x%29=200%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2C0.6x%2B2%28135-x%29=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2C0.6x%2B270-2x=200%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2C0.6x%2B270-2x=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2C0.6x-2x=200-270%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2C0.6x-2x=200-270%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2C-1.4x=-70%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2C-1.4x=-70%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2Cx=%28-70%29%2F%28-1.4%29%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2Cx=%28-70%29%2F%28-1.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-x%2Cx=50%29 ALIGN=MIDDLE  ALT=\"system%28y=135-x%2Cx=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=135-50%2Cx=50%29 ALIGN=MIDDLE  ALT=\"system%28y=135-50%2Cx=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=85%2Cx=50%29 ALIGN=MIDDLE  ALT=\"system%28y=85%2Cx=50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6x%2B2y=200 ALIGN=MIDDLE  ALT=\"0.6x%2B2y=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the only equation you can write from the information given,<BR>\n" );
document.write( "we should expect to find more than one solution.<BR>\n" );
document.write( "Only fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > must both be integers keeps the problem from having <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6x%2B2y=200 ALIGN=MIDDLE  ALT=\"0.6x%2B2y=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3x%2By=100 ALIGN=MIDDLE  ALT=\"0.3x%2By=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=100-0.3x ALIGN=MIDDLE  ALT=\"y=100-0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be an integer, we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3x ALIGN=MIDDLE  ALT=\"0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >} to be an integer,<BR>\n" );
document.write( "and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3x=3x%2F10 ALIGN=MIDDLE  ALT=\"0.3x=3x%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to be an integer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So we take non-negative values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that can be divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=100-0.3x ALIGN=MIDDLE  ALT=\"y=100-0.3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > value,<BR>\n" );
document.write( "and tabulate all the many solutions we find:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%282%2C12%2C%0D%0Ax%2C0%2C1%2C2%2C3%2C4%2C5%2C%22.....%22%2C300%2C310%2C320%2C330%2C%0D%0Ay%2C100%2C97%2C94%2C91%2C88%2C85%2C%22.....%22%2C10%2C7%2C4%2C1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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