document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295960>Question 295960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve the following problem? I need 100 pounds of mixed nuts (peanuts and cashews). The peanuts will cost me $3.00 per pound and the cashews will cost me $4.00 per pound. How do I find out how many pounds of each kind of nut I should buy? How can I set up a system of equations to find the correct solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213329 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=213329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = pounds of peanuts<BR>\n" );
document.write( "c = pounds of cashews<BR>\n" );
document.write( "3p = cost for peanuts<BR>\n" );
document.write( "4c = cost for cashews\r<BR>\n" );
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document.write( "Your equations are:\r<BR>\n" );
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document.write( "p + c = 100 (you need 100 pounds of mixed nuts)<BR>\n" );
document.write( "3p + 4c = x (it will cost you x number of dollars)\r<BR>\n" );
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document.write( "You need to find a value for x which you will be able to spend.\r<BR>\n" );
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document.write( "x will have to be greater than or equal to $300 (all peanuts).<BR>\n" );
document.write( "x will have to be less than or equal to $400 (all cashews).\r<BR>\n" );
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document.write( "Assume x is $375.00\r<BR>\n" );
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document.write( "This means that you can spend $375.00 on mixed nuts.\r<BR>\n" );
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document.write( "Your formulas become:\r<BR>\n" );
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document.write( "p + c = 100<BR>\n" );
document.write( "3p + 4c = 375\r<BR>\n" );
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document.write( "You would then solve these 2 equations simultaneously to find out how many pounds of peanuts and cashews you can buy.\r<BR>\n" );
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document.write( "Multiply the first equation by 3 to get:\r<BR>\n" );
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document.write( "3p + 3c = 300<BR>\n" );
document.write( "3p + 4c = 375\r<BR>\n" );
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document.write( "Subtract the first equation from the second equation to get:\r<BR>\n" );
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document.write( "c = 75\r<BR>\n" );
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document.write( "Since p + c = 100, this means that p = 25.\r<BR>\n" );
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document.write( "Total cost would be 25*3 + 75*4 = 75 + 300 = $375.00.\r<BR>\n" );
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document.write( "With $375.00, you can buy 25 pounds of peanuts and 75 pounds of cashews.\r<BR>\n" );
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document.write( "If you only had $325 to spend, then your equations would have been:\r<BR>\n" );
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document.write( "p + c = 100<BR>\n" );
document.write( "3p + 4c = 325\r<BR>\n" );
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document.write( "Multiply first equation by 3 to get:\r<BR>\n" );
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document.write( "3p + 3c = 300<BR>\n" );
document.write( "3p + 4c = 325\r<BR>\n" );
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document.write( "Subtract first equation from second equation to get:\r<BR>\n" );
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document.write( "c = 25\r<BR>\n" );
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document.write( "If c = 25, then p = 75, because p + c = 100\r<BR>\n" );
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document.write( "Total cost would be 75*3 + 25*4 = 225 + 100 = $325.00\r<BR>\n" );
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document.write( "If you had $325.00 to spend, you could buy 75 pounds of peanuts and 25 pounds of cashews.\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "With $375 to spend, you could buy 25 pounds of peanuts and 75 pounds of cashews.<BR>\n" );
document.write( "With $325 to spend, you could buy 75 pounds of peanuts and 25 pounds of cashews.\r<BR>\n" );
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document.write( "The amount of money you had to spend between $300 and $400 determines how many pounds of peanuts you can buy versus how many pounds of cashews you can buy in order to get 100 pounds of mixed nuts.\r<BR>\n" );
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document.write( "If you had less than $300 to spend, you would not be able to buy 100 pounds, no matter what mix you chose.\r<BR>\n" );
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document.write( "If you had more than $400 to spend, you would have money left over, no matter what mix you chose.\r<BR>\n" );
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document.write( "You only needed between $300 and $400 in order for the pounds to be equal to 100 pounds and no money to be left over. </SPAN>\n" );
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