document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196702>Question 1196702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mike wants to make 10 ml of a 69% sugar solution by mixing together a 25% sugar solution and a 80% sugar solution.  How much of each solution must he use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829654 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=829654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows the setup for solving the problem by the standard method for \"mixture\" problems.  Of course you want to use a method something like that if a formal algebraic solution is required.<br><BR>\n" );
document.write( "But in problems like this where the numbers are \"nice\" -- as they are in this problem -- a quick and easy solution can be obtained by seeing where the percentage of the mixture lies between the percentages of the two ingredients.<br><BR>\n" );
document.write( "Look at the three percentages (on a number line, if it helps) and observe/calculate that 69 is 44/55 = 4/5 of the way from 25 to 80.  That means 4/5 of the mixture needs to be the 80% ingredient.<br><BR>\n" );
document.write( "Since the mixture is to be 10 ml, that means using 8 ml of the 80% sugar solution and 2 ml of the 25% sugar solution.<br><BR>\n" );
document.write( "ANSWER: 8 ml of the 80% solution; 2 ml of the 25% solution<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".80(8)+.25(2) = 6.4+.5 = 6.9<BR>\n" );
document.write( ".69(10) = 6.9<br><BR>\n" );
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document.write( "Postscript....<br><BR>\n" );
document.write( "If this method of solving the problem looks like magic, observe that the formal solution from the other tutor arrives at that same fraction 44/55 for the fraction of the mixture that must be the 80% sugar solution....<br><BR>\n" );
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