document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389463>Question 389463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a chemist mixes a solution that is 14% alcohol with a solution that is 22% alcohol to make 200 milliliters of a solution that is 17.6% alcohol. How many milliliters of each solution does the chemist use in the mixture? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275985 by </B><A HREF=/tutors/aboutme.mpl?userid=gwendolyn><B>gwendolyn(128)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gwendolyn><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=gwendolyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A be the amount of 14% alcohol.<BR>\n" );
document.write( "Let B be the amount of 22% alcohol.\r<BR>\n" );
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document.write( "We know the total amount is 200 ml, so:\r<BR>\n" );
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document.write( "A + B = 200<BR>\n" );
document.write( "Solving for A (picked at random):<BR>\n" );
document.write( "A + B - B = 200 - B<BR>\n" );
document.write( "A = 200 - B\r<BR>\n" );
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document.write( "Now we form another equation based on the amount of alcohol each solution contributes and the final amount:\r<BR>\n" );
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document.write( ".14 * A + .22 * B = .176 * 200\r<BR>\n" );
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document.write( ".14A + .22B = 35.2<BR>\n" );
document.write( "Multiplying everything by 100 to work with whole numbers:<BR>\n" );
document.write( "14*A + 22*B = 3520\r<BR>\n" );
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document.write( "Substiture the value of A from the first equation:\r<BR>\n" );
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document.write( "14*(200 - B) + 22*B = 3520<BR>\n" );
document.write( "2800 - 14*B + 22*B = 3520<BR>\n" );
document.write( "2800 + 8*B = 3520<BR>\n" );
document.write( "8*B = 3520 - 2800<BR>\n" );
document.write( "8*B = 720<BR>\n" );
document.write( "B = 90\r<BR>\n" );
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document.write( "Substituting the value of B back into the first equation:\r<BR>\n" );
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document.write( "A = 200 - B<BR>\n" );
document.write( "A = 200 - 90<BR>\n" );
document.write( "A = 110\r<BR>\n" );
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document.write( " </SPAN>\n" );
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