document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=719353>Question 719353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a chemist has three different acid solutions. The first acid solution contains 20% acid, the second contains 30% and the third contains 75%. He wants to use all three solutions to obtain a mixture of 68 liters containing 50% acid, using 2 times as much of the 75% solution as the 30% solution. how many liters of each solution should be used? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441368 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=441368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x amount of 20% acid<BR>\n" );
document.write( "let y amount of 30% acid<BR>\n" );
document.write( "let z amount of 75% acid\r<BR>\n" );
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document.write( "\"using 2 times as much of the 75% solution as the 30% solution. \",<BR>\n" );
document.write( "That means z/y=2/1 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=2y ALIGN=MIDDLE  ALT=\"z=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Two essential starting equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%2B30y%2B75z%29%2F68=50 ALIGN=MIDDLE  ALT=\"%2820x%2B30y%2B75z%29%2F68=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=68 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The less advanced way to solve this is to begin with the ratio between z and y and substitute into the \"two essential\" equations:\r<BR>\n" );
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document.write( "The percentage equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B7.5z=68%2A5 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B7.5z=68%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B7.5%282y%29=68%2A5 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B7.5%282y%29=68%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B15y=68%2A5 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B15y=68%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B18y=68%2A5 ALIGN=MIDDLE  ALT=\"2x%2B18y=68%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B9y=34%2A5 ALIGN=MIDDLE  ALT=\"x%2B9y=34%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solution summation equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2B%282y%29=68 ALIGN=MIDDLE  ALT=\"x%2By%2B%282y%29=68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y=68 ALIGN=MIDDLE  ALT=\"x%2B3y=68\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Our simpler system to solve is now in variables x and y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%2B9y=170%29 ALIGN=MIDDLE  ALT=\"highlight%28x%2B9y=170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%2B3y=68%29 ALIGN=MIDDLE  ALT=\"highlight%28x%2B3y=68%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the second from the first, and from resulting 6y=102, obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=17 ALIGN=MIDDLE  ALT=\"y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Use that result again in the second equation, x=68-3y, x=68-3*17, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=17 ALIGN=MIDDLE  ALT=\"x=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, go back to the given relationship between z and y, z=2y, z=2*17, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=34 ALIGN=MIDDLE  ALT=\"z=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "ANSWER SUMMARY: x=17 liters of 20%, y=17 liters of 30%, z=34 liters of 75% acid. </SPAN>\n" );
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