document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805678>Question 805678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this: How much water should be added to 30 quarts of juice that is 70% juice to get a diluted mixture that is 60% juice?\r<BR>\n" );
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document.write( "My work: Let w = the amount of water needed<BR>\n" );
document.write( "30+w= the total amount of the mixture<BR>\n" );
document.write( "100w + 2100 = 60(30+w)<BR>\n" );
document.write( "100w + 2100 = 1800 +60w<BR>\n" );
document.write( "-60w + 100w + 2100 = 1800 + 60w + (-60w)<BR>\n" );
document.write( "40w + 2100 =1800 <BR>\n" );
document.write( "-2100 + 40w + 2100 = 1800 + -2100<BR>\n" );
document.write( "40w = -300<BR>\n" );
document.write( "1/40(40w)=-300(1/40)<BR>\n" );
document.write( "w = -7.5\r<BR>\n" );
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document.write( "How can you add negative amounts of water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485399 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=485399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Wrong equation.<BR>\n" );
document.write( "The amount of juice is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7%2A30=21 ALIGN=MIDDLE  ALT=\"0.7%2A30=21\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts (70% of 30 quarts) in the undiluted juice.<BR>\n" );
document.write( "That plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of juice in the added water has to add to the amount of juice in the final dilution, which should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6%2A%2830%2Bw%29 ALIGN=MIDDLE  ALT=\"0.6%2A%2830%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of juice<BR>\n" );
document.write( "The equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6%2830%2Bw%29=0%2B0.7%2A30 ALIGN=MIDDLE  ALT=\"0.6%2830%2Bw%29=0%2B0.7%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2B0.6w=21 ALIGN=MIDDLE  ALT=\"18%2B0.6w=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6W=21-18 ALIGN=MIDDLE  ALT=\"0.6W=21-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6w=3 ALIGN=MIDDLE  ALT=\"0.6w=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=3%2F0.6 ALIGN=MIDDLE  ALT=\"w=3%2F0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=5%29 ALIGN=MIDDLE  ALT=\"highlight%28w=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The mistake:<BR>\n" );
document.write( "Using 100, 70 and 60 for 100%, 70% and 60% means that the quantities in your equation are not in quarts, but in fancy units of your invention.<BR>\n" );
document.write( "That makes it difficult to relate equations with the \"real\" situation, but we could work with that, if we prefer large numbers to decimals.<BR>\n" );
document.write( "However, if we accept your units,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2830%2Bw%29 ALIGN=MIDDLE  ALT=\"60%2830%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the amount of juice in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Bw ALIGN=MIDDLE  ALT=\"30%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of final diluted mixture,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2100=%2870%29%2830%29 ALIGN=MIDDLE  ALT=\"2100=%2870%29%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the amount of pure, undiluted juice in the initial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of original \"juice (drink) that is 70% juice\".<BR>\n" );
document.write( "However, adding to that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2100 ALIGN=MIDDLE  ALT=\"2100\"   DISABLED_style= \"max-width:90%; height:auto;\" > a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100w ALIGN=MIDDLE  ALT=\"100w\"   DISABLED_style= \"max-width:90%; height:auto;\" > term makes no sense.<BR>\n" );
document.write( "Maybe <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100w ALIGN=MIDDLE  ALT=\"100w\"   DISABLED_style= \"max-width:90%; height:auto;\" > could represent the amount of water in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of 100% pure water added, but it does not make sense to add the initial amount of pure juice plus the initial amount of pure water to find the final amount of pure juice.<BR>\n" );
document.write( "It would make more sense to add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0w ALIGN=MIDDLE  ALT=\"0w\"   DISABLED_style= \"max-width:90%; height:auto;\" >, representing the amount of juice in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarts of pure water (containing 0% juice) added. </SPAN>\n" );
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