document.write( "Question 1167782: The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $59, balcony tickets are $49, and mezzanine tickets are $34. One particular night, sales totaled $106,306. There were 254 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 444 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
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Algebra.Com's Answer #792454 by ikleyn(52784)\"\" \"About 
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\n" ); document.write( "The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine.
\n" ); document.write( "Main floor tickets are $59, balcony tickets are $49, and mezzanine tickets are $34.
\n" ); document.write( "One particular night, sales totaled $106,306. There were 254 more main floor tickets sold than balcony and mezzanine tickets combined.
\n" ); document.write( "The number of balcony tickets sold is 444 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
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\n" ); document.write( "\n" ); document.write( "            You, probably, will be very surprised, but this problem can be  EASILY  solved \r
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\n" ); document.write( "\n" ); document.write( "            using one single equation in one unknown,  as I show it below.\r
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document.write( "Let x be the number of the mezzanine tickets.\r\n" );
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document.write( "Then, according to the condition, the number of the balcony tickets is (3x + 444),\r\n" );
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document.write( "and the number of the main floor tickets is the sum  (x + (3x + 444)) + 254 = 4x + 698.\r\n" );
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document.write( "Next, you write the total money equation\r\n" );
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document.write( "    59*(4x + 698) + 49*(3x + 444) + 34*x = 106306   dollars.\r\n" );
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document.write( "Now you simply this equation and find x\r\n" );
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document.write( "    (59*4*x + 49*3*3x + 34x) + (59*698 + 49*444) = 106306\r\n" );
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document.write( "    417x                     + 62938             = 106306\r\n" );
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document.write( "    417x                                         = 106306 - 62938 = 43368\r\n" );
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document.write( "       x                                     = 43368/142 = 104.\r\n" );
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document.write( "So, 104 mezzanine tickets were sold;  3*104 + 444 = 756 balcony tickets and 4*104 + 698 = 114 main floor tickets.\r\n" );
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document.write( "It is the ANSWER, so the problem is\r\n" );
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\n" ); document.write( "\n" ); document.write( "This problem is intended for 6th grade students,  who learn solving word problems on a single unknown equations.\r
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\n" ); document.write( "\n" ); document.write( "The major goal of this  (and similar problems)  is to teach these students to make their setup using only one unknown.\r
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\n" ); document.write( "\n" ); document.write( "There are other ways to solve the problem, but they go OUT the major goal of such assignments.\r
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