document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=599145>Question 599145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A school offers a total of 9 different Latin and German courses. If the number of German courses offered at the school Is 3 less than twice the number of Latin classes, h / many Latin classes are offered at the school?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378871 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there---<BR>\n" );
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document.write( "To solve this problem, we write and solve a system of equations describing the given relationships.<BR>\n" );
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document.write( "[I] Define your variables<BR>\n" );
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document.write( "Let L be the number of Latin courses, and let G be the number of German courses.<BR>\n" );
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document.write( "[II] Write a system of equations<BR>\n" );
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document.write( "The total number of classes (Latin plus German) is 9. In algebra, we write<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BG=9 ALIGN=MIDDLE  ALT=\"L%2BG=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The phrase, \"the number of German courses...is 3 less than twice the number of Latin courses\" can be written as<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=2L-3 ALIGN=MIDDLE  ALT=\"G=2L-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "[III] Solve the system of equations<BR>\n" );
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document.write( "Re-write the first equation in terms of G.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BG=9 ALIGN=MIDDLE  ALT=\"L%2BG=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=9-L ALIGN=MIDDLE  ALT=\"G=9-L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute 9-L for G in the second equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=2L-3 ALIGN=MIDDLE  ALT=\"G=2L-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-L=2L-3 ALIGN=MIDDLE  ALT=\"9-L=2L-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify and solve for L. Add 3 to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-L%2B3=2L ALIGN=MIDDLE  ALT=\"9-L%2B3=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-L=2L ALIGN=MIDDLE  ALT=\"12-L=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add L to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=2L%2BL ALIGN=MIDDLE  ALT=\"12=2L%2BL\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12=3L ALIGN=MIDDLE  ALT=\"12=3L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 3 to isolate the variable L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F3=3L%2F3 ALIGN=MIDDLE  ALT=\"12%2F3=3L%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4 ALIGN=MIDDLE  ALT=\"L=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation L=4 means that there are 4 Latin courses. Thus there are 9-4=5 German courses (since 4+5=9.)<BR>\n" );
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document.write( "[IV] Check your work.<BR>\n" );
document.write( "Is the number of German classes 3 less than twice the number of Latin courses? Twice the number of Latin courses is 4*2=8 courses. Five is 3 less than eight. <BR>\n" );
document.write( "Check!<BR>\n" );
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document.write( "There are four Latin courses and five German courses at the school.<BR>\n" );
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document.write( "That's it! Feel free to email me via gmail if you have questions about the solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com \r<BR>\n" );
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