document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161993>Question 1161993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A candy store wishes to mix nuts selling for $2.75 per pound with nuts selling for $4.15<BR>\n" );
document.write( "per pound to make a mixture of nuts that can be sold for $3.31 per pound. How many<BR>\n" );
document.write( "pounds of nuts of each type should be mixed together to obtain 50 pounds of the mixture<BR>\n" );
document.write( "that can be sold for $3.31 per pound? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785659 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=785659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is an informal method for solving \"mixture\" problems like this that will get you to the answer to a problem like this much faster, and with much less work, than the traditional algebraic method outlined by the other tutor.<br><BR>\n" );
document.write( "Obviously, if you mix nuts worth $2.75 per pound with others worth $4.15 per pound, the value of the mixture will be somewhere between $2.75 and $4.15 per pound.  The ratio in which the two kinds of nuts are mixed exactly determines the price per pound of the mixture.<br><BR>\n" );
document.write( "And the other way around: the price per pound of the mixture exactly determines the ratio in which the two kinds of nuts are mixed.<br><BR>\n" );
document.write( "Using that concept, solve the problem like this:<br><BR>\n" );
document.write( "(1) Picturing the three prices on a number line, determine what fraction of the distance the price of the mixture is from the lower price to the higher price.<BR>\n" );
document.write( "(2) That fraction is the fraction of the mixture that needs to be the higher priced ingredient.<br><BR>\n" );
document.write( "Here are the calculations for solving this problem by that method.<br><BR>\n" );
document.write( "$2.75 to $4.15 is a difference of $1.40<BR>\n" );
document.write( "$2.75 to $3.31 is a difference of $0.56<BR>\n" );
document.write( "$0.56/$1.40 = 2/5<br><BR>\n" );
document.write( "The price of the mixture is 2/5 of the way from the lower price to the higher price; therefore, 2/5 of the mixture has to be the more expensive nuts.<br><BR>\n" );
document.write( "ANSWER: 2/5 of 50 pounds, or 20 pounds, of the more expensive nuts; the other 30 pounds of the less expensive.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "20(4.15)+30(2.75) = 83+82.50 = 165.50<BR>\n" );
document.write( "50(3.31) = 165.50<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );