document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145668>Question 1145668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "1.Mix a solution that is 30% alcohol with a solution that is 80% alcohol to make 725 mL of a solution that is 60% alcohol. How much (in mL) of each solution should you use?<BR>\n" );
document.write( "30% alcohol solution__ml<BR>\n" );
document.write( "80% alcohol solution__ml.\r<BR>\n" );
document.write( "\n" );
document.write( "2.A welder has 15 pieces of 4 ft steel angle and 18 pieces of 2 ft steel angle. What is the ratio of pieces of 4 ft steel angle to 2 ft steel angle? (Enter your answer in fraction form.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #766899 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=766899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First a standard algebraic solution to the mixture problem....<br><BR>\n" );
document.write( "x = mL of 30% alcohol solution<BR>\n" );
document.write( "725-x = mL of 80% alcohol solution<br><BR>\n" );
document.write( ".30(x) = amount of alcohol in x mL of 30% solution<BR>\n" );
document.write( ".80(725-x) = amount of alcohol in (725-x mL of 80% solution<BR>\n" );
document.write( ".60(725 = amount of alcohol in 725 mL of 60% solution<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.30%28x%29%2B.80%28725-x%29+=+.60%28725%29 ALIGN=MIDDLE  ALT=\".30%28x%29%2B.80%28725-x%29+=+.60%28725%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%28x%29+%2B+80%28725-x%29+=+60%28725%29 ALIGN=MIDDLE  ALT=\"30%28x%29+%2B+80%28725-x%29+=+60%28725%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30x+%2B+58000-80x+=+43500 ALIGN=MIDDLE  ALT=\"30x+%2B+58000-80x+=+43500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14500+=+50x ALIGN=MIDDLE  ALT=\"14500+=+50x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+290 ALIGN=MIDDLE  ALT=\"x+=+290\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 290 mL of the 30% solution and 725-290 = 435 mL of the 80% solution.<br><BR>\n" );
document.write( "That's a perfectly good method for solving mixture problems like this.<br><BR>\n" );
document.write( "But there is a much easier way....<br><BR>\n" );
document.write( "Now a much easier solution, based on where the 60% lies between the 30% and 80%....<br><BR>\n" );
document.write( "(1) 60 is 3/5 of the way from 30 to 80 (look at the 3 numbers 30, 60, and 80 on a number line; 30 to 60 is 30; 30 to 80 is 50; 30/50 = 3/5)<BR>\n" );
document.write( "(2) Therefore, 3/5 of the mixture should be the higher percentage solution.<br><BR>\n" );
document.write( "ANSWER: 3/5 of 725 mL, or 435 mL, of 80% alcohol solution; 2/5 of 725 mL, or 290 mL, of 30% alcohol solution<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );