document.write( "Question 1116734: a theater sells tickets for a concert. tickets for lower level sell for $35 each, and tickets for upper level is 25$ each. the theater sells 350 tockets and grt 10250$ how many of each were sold? \n" ); document.write( "
Algebra.Com's Answer #731648 by ikleyn(52804)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        There are different methods to solve the problem.
\n" ); document.write( "        I will show you 3 (three) basic methods in this post.\r
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\n" ); document.write( "\n" ); document.write( "Solution  1   (the system of  2  equations approach)\r
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document.write( "Let x be the number of $35 tickets and\r\n" );
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document.write( "let y be the number of $25 tickets.\r\n" );
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document.write( "Then you have these two equations\r\n" );
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document.write( "  x +   y =   350,           (1)     (counting tickets)\r\n" );
document.write( "35x + 25y = 10250  dollars   (2)     (counting dollars)\r\n" );
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document.write( "These are your basic equations, and as soon as you got this system, the setup is completed.\r\n" );
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document.write( "There are different methods of solving such system (Substitution, Elimination, using determinants). \r\n" );
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document.write( "I will use the Substitution method here. \r\n" );
document.write( "From equation (1) express y = 350-x and substitute it into equation (2). You will get a single equation for the unknown x\r\n" );
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document.write( "35x + 25(350-x) = 10250.      (3)\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "35x + 25*350 - 25x = 10250  ====>  10x = 10250 - 25*350 = 1500  ====>  x = \"1500%2F10\" = 150.\r\n" );
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document.write( "Thus, 150  $35 tickets were sold.\r\n" );
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document.write( "Hence the number of $25 tickets was 350 - 150 = 200.\r\n" );
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document.write( "Check.  150*35 + 200*25 =  = 10250 dollars.   ! Correct. !\r\n" );
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document.write( "Answer.  150  of  the  $35 tickets  and  200  of  $25  tickets.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution  2   (one equation approach)\r
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document.write( "Let x be the number of the $35 tickets.\r\n" );
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document.write( "Then the number of the $25 tickets is (350-x),  according to the condition.\r\n" );
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document.write( "The revenue equation is\r\n" );
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document.write( "35x + 25(350-x) = 10250.     (4)\r\n" );
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document.write( "It is your basic equation in the frame of this approach,\r\n" );
document.write( "and as soon as you got this equation, the setup is completed.\r\n" );
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document.write( "Notice that this equation coincides exactly with the equation (3) of the solution 1 above.\r\n" );
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document.write( "Solve equation (4) by the same method as it was done in the Solution 1.\r\n" );
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document.write( "Surely, you will get the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution  3   (Logical analysis)\r
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document.write( "Let assume for a minute that all 350 tickets were at 35 dollars.\r\n" );
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document.write( "Then the total revenue would be 35*350 = 12250 dollars.\r\n" );
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document.write( "It is by 12250 - 10250 = 2000 dollars more than the given revenue value.\r\n" );
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document.write( "Why did we get the difference ?  - But of course, because we accounted the $25 tickets as $35 tickets.\r\n" );
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document.write( "So, this difference is due to the difference between the $35 and the $25 tickets price, which (the difference) is $35 - $25 = $10.\r\n" );
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document.write( "Then it is clear that the number of $25 tickets was  \"2000%2F10\" = 200,  exactly as in the solutions 1 and 2 above.\r\n" );
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document.write( "and you got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Congratulations !   You are now familiar with 3 methods for ticket problems solution.\r
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\n" ); document.write( "\n" ); document.write( "I suggest that algebraic methods will be your basic methods for such problems,\r
\n" ); document.write( "\n" ); document.write( "and the logical analysis method will allow you to solve the problems MENTALLY without using equations.\r
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\n" ); document.write( "To see other similar solved problems on tickets, look in the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Using systems of equations to solve problems on tickets \r
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\n" ); document.write( "\n" ); document.write( "To see how the logical method works for other similar problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on two-wheel and three-wheel bicycles\r
\n" ); document.write( "\n" ); document.write( "    - Problem on animals at a farm\r
\n" ); document.write( "\n" ); document.write( "    - Problem on pills in containers\r
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