document.write( "Question 1122922: Six hundred people attended the premiere of a motion picture. Adult tickets cost $10, and children were admitted for $3. If box office receipts totaled $2430, how many children attended the premiere? \n" ); document.write( "

Algebra.Com's Answer #739107 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "One line solution\r
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\n" ); document.write( "\n" ); document.write( "        # of adult tickets =    $\"%282430-600%2A3%29%2F%2810-3%29\"$ = 90.       (*)\r
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\n" ); document.write( "\n" ); document.write( "        # of children tickets = the rest 600-90 = 510.\r
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\n" ); document.write( "\n" ); document.write( "        Check.     3*510 + 10*90 = 2430 dollars.     ! Correct !\r
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\n" ); document.write( "\n" ); document.write( "Explanation\r
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document.write( "Let assume for a minute that all 600 visitors were children.\r\n" );
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document.write( "Then the revenue would be 600*3 = 1800 dollars, making the shortage of  2430 - 600*3 dollars, comparing with the real (given) revenue.\r\n" );
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document.write( "It is because we assumed that all tickets were at 3 dollars.\r\n" );
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document.write( "Now we should replace back some number of $3 tickets by $10 tickets.\r\n" );
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document.write( "At each such replacement, we diminish the shortage by 10-3 = 7 dollars.\r\n" );
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document.write( "So, the number of replacements is expressed exactly by the formula (*), which I used in my one line solution above.\r\n" );
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document.write( "And the number of replacements is nothing else as the number of adult tickets.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "An alternative way of solution is to reduce the problem to the system of two equations with two unknowns\r
\n" ); document.write( "\n" ); document.write( "or to a single equation for one unknown.\r
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\n" ); document.write( "\n" ); document.write( "Independently of the method, you will get the same result.\r
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\n" ); document.write( "\n" ); document.write( "Interesting, that if you apply the determinant method of solution to the system of two equations, you will get THE SAME FORMULA (*)   (!)\r
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) problems on tickets\r
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