document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760246>Question 760246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve\r<BR>\n" );
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document.write( "A chemist needs 150 milliliters of a 43% solution but has only 13% and<BR>\n" );
document.write( "58% solutions available. Find how many milliliters of each that should be<BR>\n" );
document.write( "mixed to get the desired solution.\r<BR>\n" );
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document.write( "Please show detailed steps. Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462511 by </B><A HREF=/tutors/aboutme.mpl?userid=ramkikk66><B>ramkikk66(644)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ramkikk66><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=462511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the final mix have x ml of 13% solution and y ml of 58% solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+150 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" > (it is given that the final mix is 150 ml) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+equation+%281%29 ALIGN=MIDDLE  ALT=\"+equation+%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x ml of the mix is equivalent to a 0.13x solution (13% solution of say alcohol means that 100 ml of the solution will have 13 ml of alcohol and the rest as the solvent i.e. water). \r<BR>\n" );
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document.write( "Similarly, y ml of the mix is equivalent of a 0.58x solution and contains 0.58y ml of solute.\r<BR>\n" );
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document.write( "But the final mix (150 ml) is 43% strong. i.e it contains 150*0.43 ml of the solute.\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.13x+%2B+0.58y+=+150+%2A+0.43+=+64.5 ALIGN=MIDDLE  ALT=\"0.13x+%2B+0.58y+=+150+%2A+0.43+=+64.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28equation+2%29+ ALIGN=MIDDLE  ALT=\"+%28equation+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving for simultaneous equations for x and y from equations 1 and 2, we get that x = 50 and y = 100.\r<BR>\n" );
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document.write( "(If you don't know how to solve simultaneous equations, the steps are:\r<BR>\n" );
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document.write( "eq (1) rewritten as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13x+%2B+13y+=+150%2A13+ ALIGN=MIDDLE  ALT=\"+13x+%2B+13y+=+150%2A13+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13x+%2B+13y+=+1950+ ALIGN=MIDDLE  ALT=\"+13x+%2B+13y+=+1950+\"   DISABLED_style= \"max-width:90%; height:auto;\" > eq (3)\r<BR>\n" );
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document.write( "eq (2) rewritten as: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+13x+%2B+58y+=+6450+ ALIGN=MIDDLE  ALT=\"+13x+%2B+58y+=+6450+\"   DISABLED_style= \"max-width:90%; height:auto;\" > eq (4)\r<BR>\n" );
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document.write( "Subtracting (3) from (4), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45y+=+4500+ ALIGN=MIDDLE  ALT=\"+45y+=+4500+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+100+ ALIGN=MIDDLE  ALT=\"+y+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since x + y = 150 and y = 100, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+50+ ALIGN=MIDDLE  ALT=\"+x+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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