document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191542>Question 1191542</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 19. A chemist has a can full of paint thinner that is 70% alcohol. After<BR>\n" );
document.write( "replacing 7 L of the solution with 7 L of pure alcohol, the resulting<BR>\n" );
document.write( "solution is 87.5% alcohol. How many liters does the can hold?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823345 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=823345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You can solve the problem even more easily without algebra.<br><BR>\n" );
document.write( "Although the wording disguises the problem well, this is essentially a mixture problem: you are mixing 70% alcohol with 100% alcohol to get a mixture that is 87.5% alcohol.<br><BR>\n" );
document.write( "To solve the problem, you only need to find where the 87.5% of the final mixture lies between the 70% and 100% of the two ingredients.<br><BR>\n" );
document.write( "Simple arithmetic shows that 87.5% is 17.5/30 = 7/12 of the way from 70% to 100%; that means 7/12 of the mixture is the 100% alcohol.<br><BR>\n" );
document.write( "Then, since that 7/12 of the mixture is 7 liters, the capacity of the can is 12 liters.<br><BR>\n" );
document.write( "ANSWER: 12 liters<br><BR>\n" );
document.write( "The words of explanation make this seem like a lengthy solution; but the calculations alone are quick and easy:<br><BR>\n" );
document.write( "87.5-70=17.5<BR>\n" );
document.write( "100-70=30<BR>\n" );
document.write( "17.5/30=35/60=7/12<BR>\n" );
document.write( "7/12 = 7/x<BR>\n" );
document.write( "x=12<br><BR>\n" );
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