document.write( "Question 1203093: James went to the theatre to watch a concert with his family. The theatre had 4270 seats. There were 60% fewer $50-seats than $30-seats. 50% of the $30-seats and some $50-seats were sold. A total of $47 500 was collected. How many seats were unsold? \n" ); document.write( "

Algebra.Com's Answer #838362 by ikleyn(52909) $\"\"$ $\"About$

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\n" ); document.write( "James went to the theatre to watch a concert with his family.
\n" ); document.write( "The theatre had 4270 seats.
\n" ); document.write( "There were 60% fewer $50-seats than $30-seats.
\n" ); document.write( "50% of the $30-seats and some $50-seats were sold.
\n" ); document.write( "A total of $47 500 was collected. How many seats were unsold?
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document.write( "Let x be the number of the $30-seats in the theater.\r\n" );
document.write( "Then the number of the $50-seats in the theater is (4270-x).\r\n" );
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document.write( "The problem says that\r\n" );
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document.write( "    4270-x = (1-0.6)x.    (\"There were 60% fewer $50-seats than $30-seats\")\r\n" );
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document.write( "From this equation, \r\n" );
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document.write( "    4270-x = 0.4x\r\n" );
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document.write( "    4270 = x + 0.4x\r\n" );
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document.write( "    4270 = 1.4x\r\n" );
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document.write( "    x    = 4270/1.4 = 3050.\r\n" );
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document.write( "Thus, there were 3050 of the $30-seats in the theater and (4270-3050) = 1220 of the $50-seats.\r\n" );
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document.write( "Next, 50% of the $30-seats were sold, which is 3050/2 = 1525 seats,\r\n" );
document.write( "providing 30*1525 = 45750 dollars of the total revenue.\r\n" );
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document.write( "Hence, the rest part of the revenue, or 47500-45750 = 1750 dollars, was the cost of the $50-seats sold.\r\n" );
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document.write( "So, the number of the $50-seats sold was 1750/50 = 35.\r\n" );
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document.write( "Thus, the number of the total sold seats was 1525 + 35 = 1560.\r\n" );
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document.write( "The number of unsold seats was the rest, or 4270 - 1560 = 2710.\r\n" );
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document.write( "ANSWER.  The number of the unsold seats was 2710.\r\n" );
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