document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912694>Question 912694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are making a drink that requires 19 ounces of a 34-proof whiskey. Unfortunately, all you have on hand are 23-proof and 37-proof whiskey. How much of each type of whiskey do you need to mix to create 19 ounces of a 34-proof whiskey? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553995 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need a total of 19 oz. at 34 proof<BR>\n" );
document.write( "We want to know how many oz. at 23 proof to mix with 37 proof<BR>\n" );
document.write( "a+b=19,<BR>\n" );
document.write( "0.23*a+0.37*b=0.34*19<BR>\n" );
document.write( "a=19-b<BR>\n" );
document.write( "0.23*(19-b)+0.37*b=6.46<BR>\n" );
document.write( "4.37-0.23b+0.37*b=6.46<BR>\n" );
document.write( "0.14*b=2.09<BR>\n" );
document.write( "b=14.9285714<BR>\n" );
document.write( "a=19-b<BR>\n" );
document.write( "a=4.07142857 oz. at 23 proof<BR>\n" );
document.write( "b=14.9285714 oz. at 37 proof<BR>\n" );
document.write( "check<BR>\n" );
document.write( "0.23*4.07142857+0.37*14.9285714=0.34*19<BR>\n" );
document.write( "0.93642857+5.52357143=6.46<BR>\n" );
document.write( "6.46=6.46<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "codemx1\r<BR>\n" );
document.write( "\n" );
document.write( "But you say % is half of proof<BR>\n" );
document.write( "so we divide by 2<BR>\n" );
document.write( "We need a total of 19 oz. at 17%<BR>\n" );
document.write( "We want to know how many oz. at 11.5% to mix with 18.5%<BR>\n" );
document.write( "a+b=19,<BR>\n" );
document.write( "0.115*a+0.185*b=0.17*19<BR>\n" );
document.write( "a=19-b<BR>\n" );
document.write( "0.115*(19-b)+0.185*b=3.23<BR>\n" );
document.write( "2.185-0.115b+0.185*b=3.23<BR>\n" );
document.write( "0.07*b=1.045<BR>\n" );
document.write( "b=14.9285714<BR>\n" );
document.write( "a=19-b<BR>\n" );
document.write( "a=4.07142857 oz. at 11.5%<BR>\n" );
document.write( "b=14.9285714 oz. at 18.5%<BR>\n" );
document.write( "check<BR>\n" );
document.write( "0.115*4.07142857+0.185*14.9285714=0.17*19<BR>\n" );
document.write( "0.46821429+2.76178571=3.23<BR>\n" );
document.write( "3.23=3.23<BR>\n" );
document.write( "ok<BR>\n" );
document.write( "codemx1\r<BR>\n" );
document.write( "\n" );
document.write( "Surprise! It turns out the same.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );