document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30452>Question 30452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Define variables and write a system of equations for each situation.  Solve by using substitution.\r<BR>\n" );
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document.write( "Suppose you want to join a video store. Big Video offers a special discount card that costs $9.99 for one year.  With the discount card, each video rental costs $2.49.  A discount card from Main Street Video cost $20.49 for one year.  With the Main Street Video discout card, each video rental costs $1.79. After how many video rentals is the cost the same? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17102 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Big Video has a flat rate of $9.99/yr + $2.49/rentalo<BR>\n" );
document.write( "Main Video has a flat rate of $20.49/yr + $1.79/rental<BR>\n" );
document.write( "Let y = cost of renting videos<BR>\n" );
document.write( "Let x = number of videos rented<BR>\n" );
document.write( "the equations for the first year in each case are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9.99+%2B+2.49%2Ax ALIGN=MIDDLE  ALT=\"y+=+9.99+%2B+2.49%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20.49+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"y+=+20.49+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute y in the first equation for y in the 2nd<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.99+%2B+2.49%2Ax+=+20.49+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"9.99+%2B+2.49%2Ax+=+20.49+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 9.99 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.49%2Ax+=+10.50+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"2.49%2Ax+=+10.50+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 1.79*x from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.7%2Ax+=+10.50 ALIGN=MIDDLE  ALT=\".7%2Ax+=+10.50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What that says is, assuming that the rentals from both <BR>\n" );
document.write( "stores are all done in the first year, after 15 rentals <BR>\n" );
document.write( "from each, the cost of renting is the same at each store<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "There are 4 possibilities, however<BR>\n" );
document.write( "[1] rentals from both stores are in the same year<BR>\n" );
document.write( "[2] rentals from both stores spill over into the next year<BR>\n" );
document.write( "[3] rentals from Big Video only spill over into next year<BR>\n" );
document.write( "[4] rental from Main St Video only spill over into next year<BR>\n" );
document.write( "The statement of the problem sounds like the video rentals are<BR>\n" );
document.write( "in the same time period, so I'll eliminate cases [3] & [4],<BR>\n" );
document.write( "but to cover case [2], I write new equations<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+19.98+%2B+2.49%2Ax ALIGN=MIDDLE  ALT=\"y+=+19.98+%2B+2.49%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+40.98+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"y+=+40.98+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I doubled the flat yearly cost for each store<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19.98+%2B+2.49%2Ax+=+40.98+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"19.98+%2B+2.49%2Ax+=+40.98+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.49%2Ax+=+21.00+%2B+1.79%2Ax ALIGN=MIDDLE  ALT=\"2.49%2Ax+=+21.00+%2B+1.79%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.7%2Ax+=+21.00 ALIGN=MIDDLE  ALT=\".7%2Ax+=+21.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+30 ALIGN=MIDDLE  ALT=\"x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So it would take 30 rentals for the costs to be equal if all the <BR>\n" );
document.write( "rentals did not occur in the 1st year<BR>\n" );
document.write( "I think it's kind of a trick question<BR>\n" );
document.write( "Here are graphs that illustrate cases [1] & [2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28250%2C250%2C-5%2C20%2C-5%2C60%2C+9.99+%2B+2.49x%2C20.49+%2B+1.79x%29 ALIGN=MIDDLE  ALT=\"graph%28250%2C250%2C-5%2C20%2C-5%2C60%2C+9.99+%2B+2.49x%2C20.49+%2B+1.79x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28250%2C250%2C-5%2C40%2C-5%2C100%2C+19.98+%2B+2.49x%2C40.98+%2B+1.79x%29 ALIGN=MIDDLE  ALT=\"graph%28250%2C250%2C-5%2C40%2C-5%2C100%2C+19.98+%2B+2.49x%2C40.98+%2B+1.79x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "to check solutions, case [1] <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+19.98+%2B+2.49%2A15 ALIGN=MIDDLE  ALT=\"y+=+19.98+%2B+2.49%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9.99+%2B+37.35 ALIGN=MIDDLE  ALT=\"y+=+9.99+%2B+37.35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+47.34 ALIGN=MIDDLE  ALT=\"y+=+47.34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20.49+%2B+1.79%2A15 ALIGN=MIDDLE  ALT=\"y+=+20.49+%2B+1.79%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+20.49+%2B+26.85 ALIGN=MIDDLE  ALT=\"y+=+20.49+%2B+26.85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+47.34 ALIGN=MIDDLE  ALT=\"y+=+47.34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "costs are equal as they should be<BR>\n" );
document.write( "checking case [2]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+19.98+%2B+2.49%2A30 ALIGN=MIDDLE  ALT=\"y+=+19.98+%2B+2.49%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+19.98+%2B+74.70 ALIGN=MIDDLE  ALT=\"y+=+19.98+%2B+74.70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+94.68 ALIGN=MIDDLE  ALT=\"y+=+94.68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+40.98+%2B+1.79%2A30 ALIGN=MIDDLE  ALT=\"y+=+40.98+%2B+1.79%2A30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+40.98+%2B+53.70 ALIGN=MIDDLE  ALT=\"y+=+40.98+%2B+53.70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+94.68 ALIGN=MIDDLE  ALT=\"y+=+94.68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "costs are equal   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );