document.write( "Question 1143681: Tickets to a concert that were purchased in advance cost $4.50 each, and tickets purchased at the box office on the day of the concert cost $8.00 each. The total amount of money collected in ticket sales was the same as if every ticket purchased had cost $6.00. If 180 tickets were purchased in advance, what was the total number of tickets purchased at the box office? \n" ); document.write( "

Algebra.Com's Answer #764561 by ikleyn(52776) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " This problem is for one single unknown, actually.\r
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document.write( "Let x  be the number of tickets purchased at the box office (the unknown value under the question).\r\n" );
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document.write( "Then you have this equation for total money  (the \"revenue\" equation)\r\n" );
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document.write( "    4.50*180 + 8x = 6*(180 + x).      (1)\r\n" );
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document.write( "Should I explain it in more details ?  --  I think no, since it is quite OBVIOUS: the equation is self-explanatory.\r\n" );
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document.write( "Now simplify the equation and solve it for x :\r\n" );
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document.write( "    810 + 8x = 1080 + 6x\r\n" );
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document.write( "    8x - 6x  = 1080 - 810\r\n" );
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document.write( "    2x       = 270\r\n" );
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document.write( "     x       = 270/2 = 135.\r\n" );
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document.write( "ANSWER.  135 tickets were purchased at the box office.\r\n" );
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document.write( "CHECK.   Left side of the equation (1) is  4.50*180 + 8*135 = 1890 dollars.\r\n" );
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document.write( "         Right side of the equation (1) is  6*(180 + 135) = 1890 dollars.\r\n" );
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document.write( "         Both sides of the equation (1) are equal.\r\n" );
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document.write( "         It means that the solution and the answer are CORRECT (!)\r\n" );
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