document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187739>Question 1187739</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $18. The total cost to rent 3 chairs and 8 tables is $55. What is the cost to rent each chair and each table? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818761 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let c be the rental cost for each chair<BR>\n" );
document.write( "Let t be the rental cost for each table<br><BR>\n" );
document.write( "The total cost to rent 5 chairs and 2 tables is $18:  5c + 2t = 18<br><BR>\n" );
document.write( "The total cost to rent 3 chairs and 8 tables is $55.  3c + 8t = 55<br><BR>\n" );
document.write( "(1) Solving the problem informally, using logical reasoning....<br><BR>\n" );
document.write( "Since the cost of 5 chairs and 2 tables is $18, the cost of 20 chairs and 8 tables is 4*$18 = $72.<BR>\n" );
document.write( "But the cost of 3 chairs and 8 tables is $55; the difference between the two cases is 20-3 = 17 more chairs for an additional $72-$55 = $17.  So the rental cost for each chair is $17/17 = $1.<BR>\n" );
document.write( "And then since 5 chairs at $1 each and 2 tables cost $18 to rent, the cost for the 2 tables is $13, so the cost per table is $6.50.<br><BR>\n" );
document.write( "ANSWER: $1 per chair and $6.50 per table<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "5c+2t = 5(1)+2(6.50) = 5+13 = 18<BR>\n" );
document.write( "3c+8t = 3(1)+8(6.50) = 3+52 = 55<br><BR>\n" );
document.write( "(2) Using formal algebra....<br><BR>\n" );
document.write( "5c + 2t = 18<BR>\n" );
document.write( "3c + 8t = 55<br><BR>\n" );
document.write( "Multiply the first equation by 4:<BR>\n" );
document.write( "20c + 8t = 72<br><BR>\n" );
document.write( "Compare that equation to the second original equation:<BR>\n" );
document.write( "17c = 17<br><BR>\n" );
document.write( "Solve to find the cost for each chair:<BR>\n" );
document.write( "c = 17/17 = 1<br><BR>\n" );
document.write( "Use that cost per chair in the first original equation to find the cost per table:<BR>\n" );
document.write( "5(1)+2t = 18<BR>\n" );
document.write( "5+2t = 18<BR>\n" );
document.write( "2t = 18-5 = 13<BR>\n" );
document.write( "t = 13/2 = 6.5<br><BR>\n" );
document.write( "ANSWERS: c=1; t=6.5  --  i.e.  $1 per chair and $6.50 per table<br><BR>\n" );
document.write( "Observe that the solution using formal algebra uses EXACTLY the same calculations as the informal solution.<br><BR>\n" );
document.write( "But we need to understand the formal algebraic solution, because an informal solution will not be possible when the problems get a lot more complicated.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );