document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295135>Question 295135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a word problem that says, \"Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a one time bulk purchase at a buyers club with membership fees or purchase the same goods at a conventional supermarket.\" I have to develop an algebraic equation for each option and then graph it. I believe the equations should be in the form \"y=mx+b\". I chose trail mix as an appropriate real world item to price compare, and found Sam's club membership fees to be 35.00, and Sam's club trail mix to cost 7.48 for a 48oz bag. I went to Walmart supercenter to compare and their biggest bag is 28 oz for 4.98. So the two equations I have are y=(4.98/28)x+o for walmart and y=(7.98/48)x+35 for Sam's club. Is this correct? I'm not sure if I'm factoring in the membership fee correctly. Thank you for taking the time to help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212759 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=212759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Price at Sam's would be:\r<BR>\n" );
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document.write( "$35.00 + $7.48 per 48 ounce bag.\r<BR>\n" );
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document.write( "Price at Walmart would be:\r<BR>\n" );
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document.write( "$4.98 per 28 ounce bag.\r<BR>\n" );
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document.write( "You have 2 equations.\r<BR>\n" );
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document.write( "y = (4.98/28)*x for Walmart.\r<BR>\n" );
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document.write( "y = $35.00 + (7.48/48)*x for Sam's.\r<BR>\n" );
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document.write( "It looks like your equations are correct.\r<BR>\n" );
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document.write( "To look for a break even point, you would set these equations equal to each other.\r<BR>\n" );
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document.write( "You would get:\r<BR>\n" );
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document.write( "(4.98/28) * x = 35 + (7.48/48) * x\r<BR>\n" );
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document.write( "You would subtract (7.48/48) * x from both sides of this equation to get:\r<BR>\n" );
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document.write( "(4.98/28) * x - (7.48/48) * x = 35\r<BR>\n" );
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document.write( "You would factor out the x to get:\r<BR>\n" );
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document.write( "x * (4.98/28) - (7.48/48) = 35\r<BR>\n" );
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document.write( "You would divide 4.98/28 to get the cost per ounce, and you would divide 7.48/48 to get the cost per ounce.\r<BR>\n" );
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document.write( "You would get:\r<BR>\n" );
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document.write( "x * (.177857143 - .155833333) = 35\r<BR>\n" );
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document.write( "You would combine like terms to get:\r<BR>\n" );
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document.write( "x * (.02202381) = 35\r<BR>\n" );
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document.write( "You would divide both sides of this equation by .02202381 to get:\r<BR>\n" );
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document.write( "x = 1589.189189 ounces.\r<BR>\n" );
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document.write( "That's you break even point.\r<BR>\n" );
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document.write( "To confirm, you would substitute in your original equation to get:\r<BR>\n" );
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document.write( "(4.98/28) * x = 35 + (7.48/48) * x would become:\r<BR>\n" );
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document.write( "(4.98/28) * 1589.189189 = 35 + (7.48/48) * 1589.189189 which would become:\r<BR>\n" );
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document.write( "282.6486486 = 282.6486486 confirming that the value for x is good.\r<BR>\n" );
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document.write( "Your answer would be:\r<BR>\n" );
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document.write( "At less than 1589.189189 ounces, it would be cheaper to go to Walmart.\r<BR>\n" );
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document.write( "At greater than 1589.189189 ounces, it would be cheaper to to to Sam's.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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