document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943192>Question 943192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A MACHINE IN A POTTERY FACTORY TAKES 3 MINUTES TO FORM A BOWL AND 1 MINUTE TO FORM A PLATE. The material for a bowl cost 25 cents and material for a plate costs 20 cents . If the machine runs for 8 hours (480 minutes) and exactly 44 dollars is available to spend on materials, how many bowls and plates can be produced? \r<BR>\n" );
document.write( "\n" );
document.write( "So far I have 0.25x+0.20y=44 and 3x+y=8 is am I missing another equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575011 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=575011\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You don't say what <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;\" > mean<BR>\n" );
document.write( "I would define them as:<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of minutes the machine<BR>\n" );
document.write( "spends making bowls<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of minutes the machine <BR>\n" );
document.write( "spends making plates<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Then my equations would be:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2A%28x%2F3%29+%2B20y+=+4400+ ALIGN=MIDDLE  ALT=\"+25%2A%28x%2F3%29+%2B20y+=+4400+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( changing dollars to cents )<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+=+480+ ALIGN=MIDDLE  ALT=\"+x+%2B+y+=+480+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25x+%2B+60y+=+13200+ ALIGN=MIDDLE  ALT=\"+25x+%2B+60y+=+13200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+12y+=+2640+ ALIGN=MIDDLE  ALT=\"+5x+%2B+12y+=+2640+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+ ALIGN=MIDDLE  ALT=\"+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "subtract (2) from (1)<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x+%2B+12y+=+2640+ ALIGN=MIDDLE  ALT=\"+5x+%2B+12y+=+2640+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5x+-+5y+=+-2400+ ALIGN=MIDDLE  ALT=\"+-5x+-+5y+=+-2400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+=+240+ ALIGN=MIDDLE  ALT=\"+7y+=+240+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+34.286+ ALIGN=MIDDLE  ALT=\"+y+=+34.286+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+=+480+ ALIGN=MIDDLE  ALT=\"+x+%2B+y+=+480+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+445.714+ ALIGN=MIDDLE  ALT=\"+x+=+445.714+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2F3+=+148.571+ ALIGN=MIDDLE  ALT=\"+x%2F3+=+148.571+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like the machine makes<BR>\n" );
document.write( "148 bowls and 34 plates<BR>\n" );
document.write( "( can't make fractions of them )<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2A%28x%2F3%29+%2B20y+=+4400+ ALIGN=MIDDLE  ALT=\"+25%2A%28x%2F3%29+%2B20y+=+4400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2A148.571+%2B20%2A34.286+=+4400+ ALIGN=MIDDLE  ALT=\"+25%2A148.571+%2B20%2A34.286+=+4400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3714.28+%2B+685.72+ ALIGN=MIDDLE  ALT=\"+3714.28+%2B+685.72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4400+=+4400+ ALIGN=MIDDLE  ALT=\"+4400+=+4400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+y+=+480+ ALIGN=MIDDLE  ALT=\"+x+%2B+y+=+480+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+445.714+%2B+34.286+=+480+ ALIGN=MIDDLE  ALT=\"+445.714+%2B+34.286+=+480+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+480+=+480+ ALIGN=MIDDLE  ALT=\"+480+=+480+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Check my math, assumptions, and conclusions<BR>\n" );
document.write( "carefully. I have been WAY off base before.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );