document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242798>Question 242798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The fun guys game rental store chargesan annual fee of $10 plus $3.50 per game rented. The game bank the annual fee of $22 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is the cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177764 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=177764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Define your terms:<BR>\n" );
document.write( "x = number of game bank rentals<BR>\n" );
document.write( "f = cost of fun guys game rentals = $10 + $3.50 * x = 10 + 3.5x.<BR>\n" );
document.write( "g = cost of game bank rentals = $22 + $2.50 * x = 22 + 2.5x.<BR>\n" );
document.write( "The question actually asks 2 questions<BR>\n" );
document.write( "1) What value of x makes the costs the same?  <BR>\n" );
document.write( "2) What is the cost?<BR>\n" );
document.write( "Answering questions:<BR>\n" );
document.write( "To test the value of x that makes the costs equal, set the equations equal to one another.<BR>\n" );
document.write( "10 + 3.5x = 22 + 2.5x<BR>\n" );
document.write( "Subtracting 2.5x from both sides.<BR>\n" );
document.write( "10 + 1x = 22.  (Note that 1x is typically shown as just 'x'.)<BR>\n" );
document.write( "Subtracting 10 from both sides.<BR>\n" );
document.write( "x = 22 - 10 = 12.<BR>\n" );
document.write( "Check your work by substituting in for values you don't know.<BR>\n" );
document.write( "f = 10 + 3.5(12) = 10 + 42 = 52<BR>\n" );
document.write( "g = 22 + 2.5(12) = 22 + 30 = 52<BR>\n" );
document.write( "That shows the value x = 12 solves both.<BR>\n" );
document.write( "And checking the solutions reveals the answer to the second question:  $52.<BR>\n" );
document.write( "An interesting third question is:  Which is the better value?<BR>\n" );
document.write( "Since the annual dues are paid just once, after you rent at least 12 games per year, the game bank is cheaper per rental:  $2.50 vs. the $3.50 charged by the fun guys.<BR>\n" );
document.write( "So, IF you plan to rent at least 12 games per year (or 1 per month), then the game bank is less costly.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );