document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197109>Question 1197109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> vip seating reserved seating and general admission tickets were sold for the school play at $15 $10 and 5$ each respectively the drama department sold 360 tickets for a total of $2800 if there were 40 more general admission tickets than the total number of vip and reserved tickets how many of each type of ticket were sold </SPAN>\n" );
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document.write( "Start with this: the total number of tickets is 360, and the number of general admission tickets was 40 more than the rest.<br><BR>\n" );
document.write( "Use formal algebra if you want; or use logical reasoning and simple arithmetic to determine that 200 of the 360 tickets were general admission.<br><BR>\n" );
document.write( "Those 200 general admission tickets cost a total of 200($5) = $1000, meaning the other 160 tickets cost a total of $2800-$1000 = $1800.<br><BR>\n" );
document.write( "You can then use formal algebra to set up a pair of equations to find the numbers of VIP seating tickets and reserved seating tickets -- something like<br><BR>\n" );
document.write( "x+y = 160  (total number of tickets)<BR>\n" );
document.write( "15x+10y=1800  (total cost of the tickets)<br><BR>\n" );
document.write( "That system of equations is easily solved by any of several standard algebraic techniques.<br><BR>\n" );
document.write( "But this remaining part of the problem can also be solved using logical reasoning and simple arithmetic, as follows.<br><BR>\n" );
document.write( "(1) If all 160 remaining tickets were reserved seating tickets, their total cost would have been $1600<BR>\n" );
document.write( "(2) But the actual cost is $1800, which is $200 more<BR>\n" );
document.write( "(3) Each VIP seating ticket costs $5 more than each reserved seating ticket<BR>\n" );
document.write( "(4) To make the additional $200, the number of VIP seating tickets had to be 200/5 = 40<br><BR>\n" );
document.write( "So of the remaining 160 tickets, 40 were VIP seating tickets, meaning 120 were reserved seating tickets.<br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "VIP seating: 40<BR>\n" );
document.write( "reserved seating: 120<BR>\n" );
document.write( "general admission: 200<br><BR>\n" );
document.write( "CHECK: 40(15)+120(10)+200(5) = 600+1200+1000 = 2800<br><BR>\n" );
document.write( " </SPAN>\n" );
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