document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198083>Question 1198083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Grapefruit costs 50 cents per 12 ounce can, and pineapple costs 85 cents per 12 ounce can.  How many of each should she mix to obtain 84 ounces of a mixture that will cost 70 cents for every 12 ounces? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831614 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=831614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a standard algebraic solution method.<br><BR>\n" );
document.write( "Here is a much faster and easier way to solve any 2-part mixture problem like this -- if you understand it, and if a formal algebraic solution is not required.<br><BR>\n" );
document.write( "Look at the three costs per 12 ounces -- 50, 70, and 85 -- (on a number line, if it helps) and observe/calculate that 70 is 20/35 = 4/7 of the way from 50 to 85.<br><BR>\n" );
document.write( "That means 4/7 of the mixture must be the higher priced ingredient.  So...<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "pineapple: (4/7) of 84 ounces = 4*12 = 48 ounces<BR>\n" );
document.write( "grapefruit: (3/7) of 84 ounces = 3*12 = 36 ounces<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "48(85)+36(50) = 4080+1800=5880<BR>\n" );
document.write( "84(70) = 5880<br><BR>\n" );
document.write( " </SPAN>\n" );
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