document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203535>Question 1203535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You need to strengthen a 22% alcohol solution with a pure alcohol solution to obtain a 70% solution. How much pure alcohol should you add to 100 milliliters of the 22% solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839176 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The standard algebraic solution looks something like this:<br><BR>\n" );
document.write( "100 ml of 22% alcohol, plus x ml of 100% alcohol, yields (100+x) ml of 70% alcohol.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.22%28100%29%2B1.00%28x%29=.70%28100%2Bx%29 ALIGN=MIDDLE  ALT=\".22%28100%29%2B1.00%28x%29=.70%28100%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2Bx=70%2B.7x ALIGN=MIDDLE  ALT=\"22%2Bx=70%2B.7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3x=48 ALIGN=MIDDLE  ALT=\".3x=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=48%2F.3=160 ALIGN=MIDDLE  ALT=\"x=48%2F.3=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 160 ml<br><BR>\n" );
document.write( "Here is an alternative, informal method which often makes reaching the answer easier.<br><BR>\n" );
document.write( "Picture a number line showing the three percentages -- 22, 70, and 100.  Calculate that 70 is 48/78 of the way from 22 to 100 (22 to 70 is a difference of 48; 22 to 100 is a difference of 78).<br><BR>\n" );
document.write( "That fraction 48/78 means the two ingredients must be mixed in the ratio 48:(78-48) = 48:30 = 8:5. Since 70% is closer to 100% than to 22%, the larger portion must be the 100% alcohol.  Then we have the proportion<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%3A5=x%3A100 ALIGN=MIDDLE  ALT=\"8%3A5=x%3A100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=800 ALIGN=MIDDLE  ALT=\"5x=800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=160 ALIGN=MIDDLE  ALT=\"x=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And again of course the answer is 160 ml.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );