document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189249>Question 1189249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A factory sorts pencils into bags such that 19 large bags plus 3 small bags contain a total of 224 pencils. The sum of the number of pencils in a large bag plus the number in a small bag is:<BR>\n" );
document.write( "A)16   B)36  c)42  D)19   E)18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820570 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are some great answers already. I'll post a different viewpoint.\r<BR>\n" );
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document.write( "L = number of pencils in one large bag<BR>\n" );
document.write( "s = number of pencils in one small bag\r<BR>\n" );
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document.write( "3s = number of pencils from the three small bags only<BR>\n" );
document.write( "19L = number of pencils from the 19 large bags only<BR>\n" );
document.write( "19L+3s = number of pencils total from all bags mentioned<BR>\n" );
document.write( "19L+3s = 224<BR>\n" );
document.write( "This is one of the equations in the system.\r<BR>\n" );
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document.write( "The goal is to find the number k such that L+s = k<BR>\n" );
document.write( "We're given five possible answer choices: {16,36,42,19,18}. The value k takes on one of those numbers.\r<BR>\n" );
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document.write( "If k = 16, then we have this system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2Bs+=+16%2C19L%2B3s+=+224%29 ALIGN=MIDDLE  ALT=\"system%28L%2Bs+=+16%2C19L%2B3s+=+224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving that system leads to (L,s) = (11,5)<BR>\n" );
document.write( "So this is one possible solution.\r<BR>\n" );
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document.write( "If k = 36, then we have this system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2Bs+=+36%2C19L%2B3s+=+224%29 ALIGN=MIDDLE  ALT=\"system%28L%2Bs+=+36%2C19L%2B3s+=+224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving that system leads to (L,s) = (7.25,28.75)<BR>\n" );
document.write( "We can rule this out because L and s must be positive whole numbers.\r<BR>\n" );
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document.write( "If k = 42, then we have this system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2Bs+=+42%2C19L%2B3s+=+224%29 ALIGN=MIDDLE  ALT=\"system%28L%2Bs+=+42%2C19L%2B3s+=+224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving that system leads to (L,s) = (6.13,35.88)<BR>\n" );
document.write( "This can be ruled out for similar reasoning as above.\r<BR>\n" );
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document.write( "If k = 19, then we have this system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2Bs+=+19%2C19L%2B3s+=+224%29 ALIGN=MIDDLE  ALT=\"system%28L%2Bs+=+19%2C19L%2B3s+=+224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving that system leads to (L,s) = (10.44,8.56)<BR>\n" );
document.write( "This can be ruled out for similar reasoning as above.\r<BR>\n" );
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document.write( "If k = 18, then we have this system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L%2Bs+=+18%2C19L%2B3s+=+224%29 ALIGN=MIDDLE  ALT=\"system%28L%2Bs+=+18%2C19L%2B3s+=+224%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving that system leads to (L,s) = (10.63,7.38)<BR>\n" );
document.write( "This can be ruled out for similar reasoning as above.\r<BR>\n" );
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document.write( "In short, choices B through E can be ruled out because they lead to L & S being nonwhole decimal numbers. Only choice A is valid.\r<BR>\n" );
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document.write( "I skipped the steps in solving each system, so let me know if you need to see those steps. <BR>\n" );
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