document.write( "Question 1203711: A movie theater has a seating capacity of 367. The theater charges $5.00 for children, $7.00 for students, and the $12.00 for adults. There are half as many adults as there are children if the total tickets sales was $2668, how many children, students, and adults attended? \n" ); document.write( "

Algebra.Com's Answer #839503 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "A movie theater has a seating capacity of 367.
\n" ); document.write( "The theater charges $5.00 for children, $7.00 for students, and the $12.00 for adults.
\n" ); document.write( "There are half as many adults as there are children if the total tickets sales was $2668,
\n" ); document.write( "how many children, students, and adults attended?
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\n" ); document.write( "\n" ); document.write( "        It may seem amazing, but the problem can be solved using only one unknown \r
\n" ); document.write( "\n" ); document.write( "        and one equation. I will show this solution method below.\r
\n" ); document.write( "\n" ); document.write( "        Surely, the theater is considered to be fully filled, as it is usually \r
\n" ); document.write( "\n" ); document.write( "        assumed in such problems, by default and from context.\r
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document.write( "Let x be the number of adults.\r\n" );
document.write( "Then the number of children is 2x, from the problem,\r\n" );
document.write( "and the number of students is (367-x-2x) = (367-3x).\r\n" );
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document.write( "Write the total money equation\r\n" );
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document.write( "    5*(2x) + 7*(367-3x) + 12x = 2668  dollars.\r\n" );
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document.write( "Simplify this equation and find x\r\n" );
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document.write( "    10x + 7*367 - 21x + 12x = 2668\r\n" );
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document.write( "    10x         - 21x + 12x = 2668 - 7*367\r\n" );
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document.write( "            x               =     99.\r\n" );
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document.write( "ANSWER.  99 adults;  2*99 = 198 children,  and  367-99-198 = 70 students.\r\n" );
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document.write( "CHECK the total money: 99*12 + 198*5 + 70*7 = 2668  doll;ars.    ! correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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The lesson to learn:

        This problem seem to be solved using three (or two) unknown;\r
\n" ); document.write( "\n" ); document.write( "         but in reality, it can be solved using one unknown and one equation,\r
\n" ); document.write( "\n" ); document.write( "         saving your time and diminishing the number of erros.\r
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\n" ); document.write( "\n" ); document.write( "         Your task is to learn to recognize such problems from the first glance.\r
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