document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98428>Question 98428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manager sell peanuts for $2.50 per pound. He wants to mix cashews that sell for $5.00 a pound with the peanuts to create 30 pounds of a mixture that sells for $4.00 a pound. How many pounds of each nut are needed.<BR>\n" );
document.write( "please show me how to set this up and solve it </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71600 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, you can start by assigning variables to the unknown quantities.<BR>\n" );
document.write( "Let P = the number of pounds of peanuts at $2.50 per pound.<BR>\n" );
document.write( "Let C = the number of pounds of cashews at $5.00 per pound.<BR>\n" );
document.write( "From the problem description, you are told that P + C = 30 pounds and this mixture will cost $4.00 per pound.<BR>\n" );
document.write( "We have enough information to set up the necessary equation, but there are two unknowns and only one equation. We need to reduce the number of unknowns to only one.<BR>\n" );
document.write( "$2.50(P) + $5.00(C) = $4.00(30) but you are also told that:<BR>\n" );
document.write( "P + C = 30 which can be written as C = 30 -P so we'll replace the C with 30-P.<BR>\n" );
document.write( "$2.50(P) + $5.00(30-p) = $4.00(30) Now you can simplify this and solve for P.<BR>\n" );
document.write( "2.5P+5(30-P) = 4(30)<BR>\n" );
document.write( "2.5P+150-5P = 120 Combining like-terms, we get:<BR>\n" );
document.write( "-2.5P = -30 Divide both sides by -2.5<BR>\n" );
document.write( "P = 12 You will need 12 pounds of peanuts.<BR>\n" );
document.write( "C = 30-P<BR>\n" );
document.write( "C = 30-12<BR>\n" );
document.write( "C = 18 You will need 18 pounds of cashews.\r<BR>\n" );
document.write( "\n" );
document.write( "Check:<BR>\n" );
document.write( "Cost of 12 pounds of peanuts + cost of 18 pounds of cashews = cost 0f 30 pounds of mixed nuts at $4.00 per pound.<BR>\n" );
document.write( "$2.50(12) + $5.00(18) = $4.00(30)<BR>\n" );
document.write( "$30.00 + $90.00 = $120<BR>\n" );
document.write( "$120.00 = $120.00 </SPAN>\n" );
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