document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103624>Question 103624</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/032115892x/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A radiator holds 4 gallons of fluid. If it is fullwith a 20% solution how muchfluid should be drained and replaced with a 70% antifreeze mixture to result in a 50% mixture of antifreeze? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75344 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=75344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start by assigning a variable to the unknown quantity.<BR>\n" );
document.write( "Let x = the number of gallons that you need to remove and replace.<BR>\n" );
document.write( "Now, when you remove x gallons from the radiator that presently holds 4 gallons of 20% solution, you can show this algebraically as: (After changing the percentages to their decimal equivalents) <BR>\n" );
document.write( "(4-x)(0.2)<BR>\n" );
document.write( "Following this, you want to add back the same amount but this time it will be x gallons of 70% solution, right? This can be shown as:<BR>\n" );
document.write( "+x(0.7)<BR>\n" );
document.write( "After the addition of the x gallons of 70% (0.7) solution, you expect to have 4 gallons of 50% (0.5) solution. So, putting this all together, you have:<BR>\n" );
document.write( "(4-x)(0.2)+x(0.7) = 4(0.5) Now you can simplify this and solve for x.<BR>\n" );
document.write( "0.8-0.2x+0.7x = 2 Combine like-terms.<BR>\n" );
document.write( "0.8+0.5x = 2 Subtract 0.8 from both sides.<BR>\n" );
document.write( "0.5x = 1.2 Finally, divide both sides by 0.5<BR>\n" );
document.write( "x = 2.4\r<BR>\n" );
document.write( "\n" );
document.write( "Solution (no pun intended!): You need to drain 2.4 gallons of the 20% solution and replace it with 2.4 gallons of 70% soltion to obtain 4 gallons of 50% solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );