document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134775>Question 134775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the problem using three variables.\r<BR>\n" );
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document.write( "A company sells nuts in bulk quantities.  When bought in bulk, peanuts sell for $1.50 per pound, almonds $2.25 per pound, and cashews for $3.75 per pound.  Suppose a specialty shop wants a mixture of 270 pounds that will cost $2.89 per pound.  Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is twice the number of pounds of peanuts.  Round your answer to the nearest pound.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98656 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the problem using three variables. <BR>\n" );
document.write( "A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.50 per pound, almonds $2.25 per pound, and cashews for $3.75 per pound. Suppose a specialty shop wants a mixture of 270 pounds that will cost $2.89 per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is twice the number of pounds of peanuts. Round your answer to the nearest pound.<BR>\n" );
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document.write( "Let a = lbs of almonds<BR>\n" );
document.write( "Let c = lbs of cashews<BR>\n" );
document.write( "Let p = lbs of peanuts<BR>\n" );
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document.write( "2.25a + 3.75c + 1.50p = 2.89(270)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "a + c + p = 270<BR>\n" );
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document.write( "It says,\"the sum of the number of pounds of almonds and cashews is twice the number of pounds of peanuts.\"<BR>\n" );
document.write( "2p =(a+c)<BR>\n" );
document.write( "p = .5(a+c)<BR>\n" );
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document.write( "Substitute .5(a+c) for p in the two equations<BR>\n" );
document.write( "2.25a + 3.75c + 1.50(.5(a+c)) = 2.89(270)<BR>\n" );
document.write( "2.25a + 3.75c + .75a + .75c = 780.3<BR>\n" );
document.write( "3a + 4.5c = 780.3<BR>\n" );
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document.write( "a + b + .5(a+b) = 270<BR>\n" );
document.write( "a + b + .5a + .5b = 270<BR>\n" );
document.write( "1.5a + 1.5b = 270<BR>\n" );
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document.write( "Multiply the above by 2 and subtract from 1st equation<BR>\n" );
document.write( "3a + 4.5c = 780.3<BR>\n" );
document.write( "3a + 3.0c = 540<BR>\n" );
document.write( "----------------subtracting eliminates a<BR>\n" );
document.write( "0a + 1.5c = 240.3<BR>\n" );
document.write( "c = 240.3/1.5<BR>\n" );
document.write( "c = 160.2 ~ 160 lb of cashews<BR>\n" );
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document.write( "use equation 3a + 3c = 540 to find a<BR>\n" );
document.write( "3a + 3(160.2) = 540<BR>\n" );
document.write( "3a + 480.6 = 540<BR>\n" );
document.write( "3a = 540 - 480.6<BR>\n" );
document.write( "3a = 59.4<BR>\n" );
document.write( "a = 59.4/3<BR>\n" );
document.write( "a = 19.8 ~ 20 lb of almonds <BR>\n" );
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document.write( "Find p<BR>\n" );
document.write( "20 + 160 + p = 270<BR>\n" );
document.write( "p = 270 - 180<BR>\n" );
document.write( "p = 90 lb of peanuts<BR>\n" );
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document.write( "Check solutions in 1st original equation:<BR>\n" );
document.write( "2.25(20) + 3.75(160) + 1.5(90) = 2.89(270)<BR>\n" );
document.write( "45 + 600 + 135 = 780<BR>\n" );
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document.write( "Confirms our solution of: 20 lb of almonds, 160 lb of cashews, 90 lb of peanuts </SPAN>\n" );
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