document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419129>Question 419129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A glue company needs to make some glue tat it can sell at $120 per barrel.It wants to use 150 barrels of glue worth $100 per barrel, along with glue worth $150 per barrel and and glue worth $190 per barrel.It must use the same number of barrels of $150 and $190 glue.How much of the $150 and $190 glue will be needed?How many Barrels of $120 glue will be produced?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853240 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13327)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=853240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Another tutor has provided a standard formal algebraic solution to the problem.  But the numbers in this problem make it a good one for solving informally using logical reasoning instead of formal algebra.<br><BR>\n" );
document.write( "Since equal amounts of the glues worth $150 per barrel and $190 per barrel are to be used, the average cost of those two ingredients is halfway between those two prices, which is $170 per barrel.<br><BR>\n" );
document.write( "Then the problem becomes mixing glue worth $100 per barrel with glue worth $170 per barrel to get glue worth $120 per barrel.  The ratio in which those two ingredients must be mixed is exactly determined by where the $120 price lies between the $100 and $170 prices.<br><BR>\n" );
document.write( "The difference between $100 and $120 is $20; the difference between $120 and $170 is $50.  Those differences mean the two ingredients must be mixed in the ratio 20:50 = 2:5.<br><BR>\n" );
document.write( "Because $120 is closer to $100 than it is to $170, the larger portion must be the ingredient worth $100 per barrel.  So the mixture needs to be 5 parts of the glue worth $100 per barrel and 2 parts of the glue worth $170 per barrel.<br><BR>\n" );
document.write( "Given that there are 150 barrels of glue worth $100 per barrel, use a proportion to find that we need 60 barrels of the glue worth $170 per barrel:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%3A5=x%3A2 ALIGN=MIDDLE  ALT=\"150%3A5=x%3A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=300 ALIGN=MIDDLE  ALT=\"5x=300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=60 ALIGN=MIDDLE  ALT=\"x=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then, since the glue worth $170 per barrel is equal amounts of the glues worth $150 and $190 per barrel, there must be 30 barrels each of the $150 per barrel glue and the $190 per barrel glue.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "(1) 30 barrels each of the $150 per barrel and $190 per barrel glue will be used<BR>\n" );
document.write( "(2) The total number of barrels of glue will be 150+30+30 = 210<br><BR>\n" );
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