document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200265>Question 200265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "A biologist has two brine solutions, one containing 1% salt and another containing 4% salt. How many milliliters of each solution should he mix to obtain 1 L of a solution that contains 2.8% salt?\r<BR>\n" );
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document.write( "thanks for the homework help!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150578 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=150578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "x = amount of brine solution with 1% salt (in liters)<BR>\n" );
document.write( "y = amount of brine solution with 4% salt (in liters)\r<BR>\n" );
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document.write( "Since he's mixing the two solutions to get one liter, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1 ALIGN=MIDDLE  ALT=\"x%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, the two solutions add up to one liter.\r<BR>\n" );
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document.write( "So the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=1 ALIGN=MIDDLE  ALT=\"x%2By=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since \"x\" is the amount of the 1% solution, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01x ALIGN=MIDDLE  ALT=\"0.01x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the amount of pure salt (since 1% of the given solution is given to be salt). Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.04y ALIGN=MIDDLE  ALT=\"0.04y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the amount of pure salt (from the other solution). These figures add up to the total <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.028%28x%2By%29 ALIGN=MIDDLE  ALT=\"0.028%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: 0.028 is the percentage while x+y is the total amount). Now add up the two parts and set them equal to the last portion to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01x%2B0.04y=0.028%28x%2By%29 ALIGN=MIDDLE  ALT=\"0.01x%2B0.04y=0.028%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01x%2B0.04y=0.028%28x%2By%29 ALIGN=MIDDLE  ALT=\"0.01x%2B0.04y=0.028%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01x%2B0.04y=0.028x%2B0.028y ALIGN=MIDDLE  ALT=\"0.01x%2B0.04y=0.028x%2B0.028y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B40y=28x%2B28y ALIGN=MIDDLE  ALT=\"10x%2B40y=28x%2B28y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY number by 1000 (to move the decimal 3 spots to the right)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B40y-28x-28y=0 ALIGN=MIDDLE  ALT=\"10x%2B40y-28x-28y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to one side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18x%2B12y=0 ALIGN=MIDDLE  ALT=\"-18x%2B12y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18x%2B12y=0 ALIGN=MIDDLE  ALT=\"-18x%2B12y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%2By=1%2C-18x%2B12y=0%29 ALIGN=MIDDLE  ALT=\"system%28x%2By=1%2C-18x%2B12y=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%28x%2By%29=18%281%29 ALIGN=MIDDLE  ALT=\"18%28x%2By%29=18%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 18.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B18y=18 ALIGN=MIDDLE  ALT=\"18x%2B18y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2818x%2B18y=18%2C-18x%2B12y=0%29 ALIGN=MIDDLE  ALT=\"system%2818x%2B18y=18%2C-18x%2B12y=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818x%2B18y%29%2B%28-18x%2B12y%29=%2818%29%2B%280%29 ALIGN=MIDDLE  ALT=\"%2818x%2B18y%29%2B%28-18x%2B12y%29=%2818%29%2B%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818x%2B-18x%29%2B%2818y%2B12y%29=18%2B0 ALIGN=MIDDLE  ALT=\"%2818x%2B-18x%29%2B%2818y%2B12y%29=18%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B30y=18 ALIGN=MIDDLE  ALT=\"0x%2B30y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30y=18 ALIGN=MIDDLE  ALT=\"30y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2818%29%2F%2830%29 ALIGN=MIDDLE  ALT=\"y=%2818%29%2F%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30 ALIGN=MIDDLE  ALT=\"30\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B18y=18 ALIGN=MIDDLE  ALT=\"18x%2B18y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B18%283%2F5%29=18 ALIGN=MIDDLE  ALT=\"18x%2B18%283%2F5%29=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%2B54%2F5=18 ALIGN=MIDDLE  ALT=\"18x%2B54%2F5=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2818x%2B54%2Fcross%285%29%29=5%2818%29 ALIGN=MIDDLE  ALT=\"5%2818x%2B54%2Fcross%285%29%29=5%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear any fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90x%2B54=90 ALIGN=MIDDLE  ALT=\"90x%2B54=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90x=90-54 ALIGN=MIDDLE  ALT=\"90x=90-54\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 54 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90x=36 ALIGN=MIDDLE  ALT=\"90x=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=36%2F90 ALIGN=MIDDLE  ALT=\"x=36%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54 ALIGN=MIDDLE  ALT=\"54\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F5 ALIGN=MIDDLE  ALT=\"x=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F5 ALIGN=MIDDLE  ALT=\"x=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2F5 ALIGN=MIDDLE  ALT=\"y=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Which form the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{2}{5},\frac{3}{5}\right)\">.\r<BR>\n" );
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document.write( "These solutions in decimal form are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.4 ALIGN=MIDDLE  ALT=\"x=0.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.6 ALIGN=MIDDLE  ALT=\"y=0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now recall that we stated that the values of \"x\" and \"y\" are in units of liters. So this means that x=0.4 liters and y=0.6 liters\r<BR>\n" );
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document.write( "Multiply both values by 1000 to convert to milliliters: 1000*0.4=400, 1000*0.6=600\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So this means that 400 milliliters of the 1% salt solution and 600 milliliters of the 4% salt solution are needed to make a 1 L solution that is 2.8% salt.  </SPAN>\n" );
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