document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172900>Question 1172900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $33. The total cost to rent 8 chairs and 3 tables is $30. 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 #798060 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=798060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The first given rental is for 2 chairs and 5 tables, for a cost of $33.  The second is for 8 chairs and 3 tables, for a cost of $30.<br><BR>\n" );
document.write( "Observe that the second rental has 4 times as many chairs as the first.<br><BR>\n" );
document.write( "So imagine a third rental that is 4 times the first; it has 8 chairs and 20 tables, for a total of $132.<br><BR>\n" );
document.write( "Now the second and third rentals have the same numbers of chairs; the second had 3 tables and the third has 20 tables.  The difference in the number of tables is 17; and the difference in cost is $132-$30 = $102.  That means the cost of each table is $102/17 = $6.<br><BR>\n" );
document.write( "So the first rental of 2 chairs and 5 tables, for a cost of $33, includes 5($6) = $30 for the tables.  So the two chairs cost $3, and then each chair costs $1.50.<br><BR>\n" );
document.write( "ANSWERS: $6 for each table; $1.50 for each chair.<br><BR>\n" );
document.write( "A solution using formal algebra uses exactly the same calculations as the informal solution above.<br><BR>\n" );
document.write( "2c+5t = 33 (1)<BR>\n" );
document.write( "8c+3t = 30 (2)<br><BR>\n" );
document.write( "8c+20t = 132 (3) [(1), multiplied by 4]<br><BR>\n" );
document.write( "17t = 102  [the difference between (2) and (3)<BR>\n" );
document.write( "t = 6<br><BR>\n" );
document.write( "2c+5(6) = 33<BR>\n" );
document.write( "2c = 3<BR>\n" );
document.write( "c = 1.5<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );