document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534337>Question 534337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pure acid is to be added to a 10% acid solution to obtain 42 L of a 40% acid solution. What amounts of each should be used?\r<BR>\n" );
document.write( "\n" );
document.write( "blank L of pure acid solution and blank L of 10% acid solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351461 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=351461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = amount 10% acid<BR>\n" );
document.write( "y = amount of pure acid<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x+y = 42 liters<BR>\n" );
document.write( "x = 42-y<BR>\n" );
document.write( "y = 42-x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The desired solution is 42 liters of a 40% solution.  It will contain 42*.40 liters of pure acid.<BR>\n" );
document.write( "42*.4 = 16.8 liters of pure acid and 25.2 liters of solvent (probably water).<BR>\n" );
document.write( ".<BR>\n" );
document.write( "10%*x + 100%*y = 40%*42<BR>\n" );
document.write( ".1*x + y = 16.8<BR>\n" );
document.write( ".<BR>\n" );
document.write( "multiply both sides by 10 to eliminate the decimals<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x + 10y = 168<BR>\n" );
document.write( ".<BR>\n" );
document.write( "substitute for x = 42-y<BR>\n" );
document.write( ".<BR>\n" );
document.write( "42-y +10y = 168<BR>\n" );
document.write( "9y = 126<BR>\n" );
document.write( "y = 126/9 = 42/3 = 14<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 42-14<BR>\n" );
document.write( "x = 28<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check how much 'pure' acid is in the solution.<BR>\n" );
document.write( "28 * 10% acid = 2.8 liters of pure acid<BR>\n" );
document.write( "13 * 100% acid = 14 liters of pure acid<BR>\n" );
document.write( "2.8 + 14 = 16.8 liters of pure acid in the 42 liters of solution<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Answer: Mix 14 liters of pure acid and 28 liters 10% acid to make 42 liters of 40% acid.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );