document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178503>Question 1178503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The pharmacist needs 70 liters of a 55% saline<BR>\n" );
document.write( "solution. The warehouse has barrels of 10% and 80%<BR>\n" );
document.write( "saline solutions. How much of each must she mix to<BR>\n" );
document.write( "fulfill her request? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807796 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=807796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "People who write math problems are not always well versed in science.  Ignore the fact that a 55% saline solution is physically impossible; the purpose of the problem is to give the student practice solving \"mixture\" problems.<br><BR>\n" );
document.write( "If it makes you feel better, change \"saline solution\" to \"antifreeze solution\" in the statement of the problem....<br><BR>\n" );
document.write( "(a) Using formal algebra (good practice, if practice with formal algebra is the objective)....<br><BR>\n" );
document.write( "x liters of 10% solution, plus (70-x) liters of 80% solution, yields 70 liters of 55% solution:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.10%28x%29%2B.80%2870-x%29+=+.55%2870%29 ALIGN=MIDDLE  ALT=\".10%28x%29%2B.80%2870-x%29+=+.55%2870%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra; I leave that to you.<br><BR>\n" );
document.write( "(b) Using a method which is much faster and easier than formal algebra (if the speed of getting the answer is important, and formal algebra is not required)....<br><BR>\n" );
document.write( "(1) 55% is 45/70 of the way from 10% to 80%.  (picture the three percentages 10, 55, and 80 on a number line, if it helps.  From 10 to 55 is 45; from 10 to 80 is 70.)<BR>\n" );
document.write( "(2) That means 45/70 of the mixture is the 80% solution.<br><BR>\n" );
document.write( "ANSWER: 45/70 of 70 liters, or 45 liters, of 80%; the other 25 liters of 10%.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".10(25)+.80(45) = 2.5+36 = 38.5<BR>\n" );
document.write( ".55(70) = 38.5<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );