document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231252>Question 231252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rebecca wants to bake cookies and cupcakes for a bake sale. She can bake 15 cookies at a time and 12 cupcakes at a time. She needs to make at least 20 baked goods but no more than 360, and she wants to have at least three times as many cookies as cupcakes. What combination of batches of each could Rebecca make?<BR>\n" );
document.write( "I need to get two system of inequality equations from this but I am not sure if I am getting the right equations. The equations I have are: x >= 3y and 120 <= x+y <=360 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171193 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=171193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of batches of cookies she could make<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of batches of cupcakes she could make<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C=+15a+%2B+12b+%3C=+360 ALIGN=MIDDLE  ALT=\"20+%3C=+15a+%2B+12b+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%3E=+3%2A12b ALIGN=MIDDLE  ALT=\"15a+%3E=+3%2A12b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%3E=+36b ALIGN=MIDDLE  ALT=\"15a+%3E=+36b\"   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=15a+%2B+12b+%3E=+20 ALIGN=MIDDLE  ALT=\"15a+%2B+12b+%3E=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%3E=+20+-+12b ALIGN=MIDDLE  ALT=\"15a+%3E=+20+-+12b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E=+-%284%2F5%29%2Ab+%2B+4%2F3 ALIGN=MIDDLE  ALT=\"a+%3E=+-%284%2F5%29%2Ab+%2B+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%2B+12b+%3C=+360 ALIGN=MIDDLE  ALT=\"15a+%2B+12b+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%3C=+360+-+12b ALIGN=MIDDLE  ALT=\"15a+%3C=+360+-+12b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3C=+-%284%2F5%29%2Ab+%2B+24 ALIGN=MIDDLE  ALT=\"a+%3C=+-%284%2F5%29%2Ab+%2B+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%3E=+%2812%2F5%29%2Ab ALIGN=MIDDLE  ALT=\"a+%3E=+%2812%2F5%29%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I plot a on vertical, b on horizontal for these 3 equations, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C600%2C-10%2C50%2C-10%2C50%2C-%284%2F5%29%2Ax+%2B+4%2F3%2C-%284%2F5%29%2Ax+%2B+24%2C%2812%2F5%29%2Ax+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like the solution is the small triangular<BR>\n" );
document.write( "region bounded by the 3 lines and the a-axis<BR>\n" );
document.write( "If I try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=18 ALIGN=MIDDLE  ALT=\"a=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C=+15a+%2B+12b+%3C=+360 ALIGN=MIDDLE  ALT=\"20+%3C=+15a+%2B+12b+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C=+15%2A18+%2B+12%2A6+%3C=+360 ALIGN=MIDDLE  ALT=\"20+%3C=+15%2A18+%2B+12%2A6+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C=+270+%2B+72+%3C=+360 ALIGN=MIDDLE  ALT=\"20+%3C=+270+%2B+72+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C=+342+%3C=+360 ALIGN=MIDDLE  ALT=\"20+%3C=+342+%3C=+360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15a+%3E=+36b ALIGN=MIDDLE  ALT=\"15a+%3E=+36b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a+%3E=+12b ALIGN=MIDDLE  ALT=\"5a+%3E=+12b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A18+%3E=+12%2A6 ALIGN=MIDDLE  ALT=\"5%2A18+%3E=+12%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90+%3E=+72 ALIGN=MIDDLE  ALT=\"90+%3E=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope I got it right- I think so<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );