document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387536>Question 387536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chemist has only 50% and 20% sulfuric acid on his laboratory. How much of each should be mixed to obtain 12 liters of a 30% 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 #274008 by </B><A HREF=/tutors/aboutme.mpl?userid=gwendolyn><B>gwendolyn(128)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gwendolyn><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=gwendolyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <BR>\n" );
document.write( "f = amount of 50% solution used<BR>\n" );
document.write( "t = amount of 20% solution used.<BR>\n" );
document.write( "The problem states that we want a total of 12 liters of solution, so:<BR>\n" );
document.write( "f + t = 12<BR>\n" );
document.write( "We solve for f (we could solve for t, but we picked one at random):<BR>\n" );
document.write( "f = 12 - t\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can also form an equation based on the anount of acid in each term.<BR>\n" );
document.write( "The amount of acid contributed by f and the amount of acid contributed <BR>\n" );
document.write( "by t added together need to add up to the amount of acid in the final solution. <BR>\n" );
document.write( "To do this, we convert each percentage to the equivalent decimal factor<BR>\n" );
document.write( "(50% = .5; 20% = .2; 30% = .3)\r<BR>\n" );
document.write( "\n" );
document.write( "So, in equation form:\r<BR>\n" );
document.write( "\n" );
document.write( ".5f + .2t = (.3)*12<BR>\n" );
document.write( ".5f + .2t = 3.6<BR>\n" );
document.write( "Let's multiply the entire equation by 10 just so we can use whole numbers:<BR>\n" );
document.write( "5f + 2t = 36\r<BR>\n" );
document.write( "\n" );
document.write( "Now we substitute the value of f from the first equation into the second equation:\r<BR>\n" );
document.write( "\n" );
document.write( "5(12 - t) + 2t = 36<BR>\n" );
document.write( "60 - 5t + 2t = 36<BR>\n" );
document.write( "60 - 3t = 36\r<BR>\n" );
document.write( "\n" );
document.write( "Subtract 60 from both sides to isolate the term with a variable:\r<BR>\n" );
document.write( "\n" );
document.write( "60 - 3t - 60 = 36 - 60 <BR>\n" );
document.write( "-3t = -24\r<BR>\n" );
document.write( "\n" );
document.write( "Divide both sides by -3 to solve for t:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3t%2F-3%29+=+%28-24%2F-3%29 ALIGN=MIDDLE  ALT=\"%28-3t%2F-3%29+=+%28-24%2F-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 8 \r<BR>\n" );
document.write( "\n" );
document.write( "And since f = 12 - t, we can solve for f:<BR>\n" );
document.write( "f = 12 - 8<BR>\n" );
document.write( "f = 4<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );