document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955501>Question 955501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> to make a certain drink, you need to mix 200ml of concentrate with 1,2l of water. determine the ratio of concentrate to water.how much you need if you have to make up a total of 14l of this drink\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583916 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=583916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.200mL=0.2L ALIGN=MIDDLE  ALT=\"0.200mL=0.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2L ALIGN=MIDDLE  ALT=\"1.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 1,2 l<BR>\n" );
document.write( "The ratio of concentrate to water is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2%2F1.2=highlight%281%2F6=%221+%3A+6%22%29 ALIGN=MIDDLE  ALT=\"0.2%2F1.2=highlight%281%2F6=%221+%3A+6%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > part of concentrate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > parts of water.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In this problem (and in many that look like this one),<BR>\n" );
document.write( "volumes are additive, so mixing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2L ALIGN=MIDDLE  ALT=\"0.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrate and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2L ALIGN=MIDDLE  ALT=\"1.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > water<BR>\n" );
document.write( "yields <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2L%2B1.2L=1.4L ALIGN=MIDDLE  ALT=\"0.2L%2B1.2L=1.4L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the mixture.<BR>\n" );
document.write( "So, to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4L ALIGN=MIDDLE  ALT=\"1.4L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the mixture you need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2L ALIGN=MIDDLE  ALT=\"0.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrate,<BR>\n" );
document.write( "a concentrate to mix ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2%2F1.4=1%2F7=%221+%3A+7%22 ALIGN=MIDDLE  ALT=\"0.2%2F1.4=1%2F7=%221+%3A+7%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and you need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2L ALIGN=MIDDLE  ALT=\"1.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > water,<BR>\n" );
document.write( "for a water to mix ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2%2F1.4=6%2F7=%226+%3A+7%22 ALIGN=MIDDLE  ALT=\"1.2%2F1.4=6%2F7=%226+%3A+7%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14L ALIGN=MIDDLE  ALT=\"14L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the drink mixture you need<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814L%29%2A%286%2F7%29=12L ALIGN=MIDDLE  ALT=\"%2814L%29%2A%286%2F7%29=12L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of water.<BR>\n" );
document.write( "That was obvious, <BR>\n" );
document.write( "because you could make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4L ALIGN=MIDDLE  ALT=\"1.4L\"   DISABLED_style= \"max-width:90%; height:auto;\" > drink mixture<BR>\n" );
document.write( "by mixing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2L ALIGN=MIDDLE  ALT=\"0.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrate and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2L ALIGN=MIDDLE  ALT=\"1.2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > water,<BR>\n" );
document.write( "so to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.4L ALIGN=MIDDLE  ALT=\"1.4L\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14L%2F%221.4+L%22=10 ALIGN=MIDDLE  ALT=\"14L%2F%221.4+L%22=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > times as much<BR>\n" );
document.write( "you would need to mix<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A%280.2L%29=2L ALIGN=MIDDLE  ALT=\"10%2A%280.2L%29=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > concentrate and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A%281.2L%29=12L ALIGN=MIDDLE  ALT=\"10%2A%281.2L%29=12L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of water.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "NOTES:<BR>\n" );
document.write( "I prefer using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > for liter; I think it is customary for chemists like me, Maybe it is required for chemists, but I do not remember exactly why I do it.<BR>\n" );
document.write( "Also, I currently live in the USA, so I use a decimal dot instead of a decimal comma,<BR>\n" );
document.write( "and when I say a billion I mean a 1 followed by 9 zeros, which I write in groups of 3 zeros, separates by commas, as in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221%2C000%2C000%2C000%22 ALIGN=MIDDLE  ALT=\"%221%2C000%2C000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Other countries use a decimal dot, and when they mean 1 billion, they write a 1 followed by 12 zeros, which they write in groups of 3 zeros, separates by dots, as in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221.000.000.000.000%22 ALIGN=MIDDLE  ALT=\"%221.000.000.000.000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Sadly, math is not yet universal.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In real life, volumes mixed are not exactly additive (as a chemical engineering professor would tell you),<BR>\n" );
document.write( "but it is usually close enough for everyday purposes,<BR>\n" );
document.write( "and I bet your math teacher is not a chemical engineer anyway,<BR>\n" );
document.write( "and does not know that volumes could change on mixing.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );