document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109815>Question 109815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You're choosing between 2 plans at a discount warehouse. PLAN A: annual membership fee is $100 and you pay 80%of manufacturer's recommended list price. PLAN B: annual membership fee is $40 and you pay 90% mrlp. How many dollars of merchandise would you need to buy in a year to pay the same amount under both plans? What will be the cost for each plan?--------Can someone please help me with this problem? I don't know how to set this up or solve it algebraically. Thank you so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80012 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=80012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At some point in your purchases the two plans will cost the same. After that point Plan A (the<BR>\n" );
document.write( "plan with the higher initial cost of $100) will save you money.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Suppose we let P represent the manufacturers' recommended prices for items. Under Plan B<BR>\n" );
document.write( "your cost would be $40 + 0.90*P for all the items that you buy.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Under Plan A your cost would be $100 + 0.80*P for all the items that you buy.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Set these two costs equal and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "40 + 0.90*P = 100 + 0.80*P<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's collect the terms containing P on the left side and the constants on the right side.<BR>\n" );
document.write( "Begin by getting rid of the 40 on the left side by subtracting 40 from both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.90*P = 60 + 0.80*P<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then get rid of the 0.80*P on the right side by subtracting 0.80*P from both sides to reduce<BR>\n" );
document.write( "the equation to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.10*P = 60<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally solve for P by dividing both sides of this equation by 0.10 (or by multiplying<BR>\n" );
document.write( "both sides by 10) to arrive at:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "P = 60/0.1 = 600<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This tells you that when you buy $600 worth of goods at the Manufacturers' suggested retail<BR>\n" );
document.write( "prices, the cost under both plans will be the same.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's check that out. Plan A would cost you $40 + 90% of 600 and this is equal to $40<BR>\n" );
document.write( "+ 0.9*600 = $40 + $540 = $580. Had you signed up for Plan B, when you bought $600 of merchandise<BR>\n" );
document.write( "you would have spent $580.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "How about Plan A. If you bought $600 worth of merchandise under Plan A you would have spent<BR>\n" );
document.write( "a total of $100 plus 80% of $600. So you would have spent $100 + $480 = $580.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So that's your answer. If you plan on spending more than $600 at the manufacturers'<BR>\n" );
document.write( "prices you will save money by going with Plan A.  Let's check this by saying that we bought<BR>\n" );
document.write( "$1000 worth of items for the year. Under Plan B the cost would be $40 + 0.9*1000 = $40 + $900 = $940.<BR>\n" );
document.write( "But under Plan A the cost would be $100 + 0.8*1000 = $100 + $800 = $900. So you would save<BR>\n" );
document.write( "about $40 by going with Plan A.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and to see what is going on with the equations.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );