document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156383>Question 1156383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Misty wishes to obtain 85 ounces of a 40% acid solution by combining a 72% acid solution with a 25% acid solution. How much of each solution should misty use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779079 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=779079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You should understand how to solve a two-part mixture problem like this using formal algebra.  But if a formal algebraic solution is not required, there is a MUCH faster way to solve the problem.<br><BR>\n" );
document.write( "A typical algebraic solution would look something like this....<br><BR>\n" );
document.write( "x = ounces of 72% acid<BR>\n" );
document.write( "85-x = ounces of 25% acid<br><BR>\n" );
document.write( "The combined acid in the two ingredients is equal to the acid in 40% of the total 85 ounces:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.72%28x%29%2B.25%2885-x%29+=+.40%2885%29 ALIGN=MIDDLE  ALT=\".72%28x%29%2B.25%2885-x%29+=+.40%2885%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.72x%2B21.25-.25x+=+34 ALIGN=MIDDLE  ALT=\".72x%2B21.25-.25x+=+34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.47x+=+12.75 ALIGN=MIDDLE  ALT=\".47x+=+12.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12.75%2F.47+=+1275%2F47 ALIGN=MIDDLE  ALT=\"x+=+12.75%2F.47+=+1275%2F47\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount of 72% acid is 1275/47 ounces; the amount of 25% acid is 85-(1275/47) = 2720/47 ounces.  Those are ugly fractions; and we had to do a lot of ugly calculations to find them.<br><BR>\n" );
document.write( "Convert those numbers to decimals or percents if required....<br><BR>\n" );
document.write( "Here is a much faster path to the same ugly answers.<br><BR>\n" );
document.write( "On a number line, 40% is 15/47 of the way from 25% to 72%.<BR>\n" );
document.write( "That means 15/47 of the mixture needs to be the 72% acid.<BR>\n" );
document.write( "15/47 of the total 85 ounces is 1275/47 ounces.<br><BR>\n" );
document.write( " </SPAN>\n" );
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