document.write( "Question 1094912: A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3235 tickets overall. It has sold 182 more $20 tickets than $10 tickets. The total sales are $62,170. How many tickets of each kind have been sold?
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Algebra.Com's Answer #709509 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30.
\n" ); document.write( "The team has sold 3235 tickets overall. It has sold 182 more $20 tickets than $10 tickets.
\n" ); document.write( "The total sales are $62,170. How many tickets of each kind have been sold?
\n" ); document.write( "How many $10 dollar tickets were sold?
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document.write( "Let T be the number of $10-tickets sold.\r\n" );
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document.write( "Then the number of $20-tickets is (T+182), according to the condition,\r\n" );
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document.write( "and the number of $30-tickets is (3235 - T - (T+182)) = 3053-2T.\r\n" );
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document.write( "Hence, your \"money equation\" is \r\n" );
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document.write( "10T + 20*(T+182) + 30*(3053-2T) = 62170.\r\n" );
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document.write( "Simplify and solve for T:\r\n" );
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document.write( "(10T + 20T - 60T) = 62170 - 20*182 - 30*3053,\r\n" );
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document.write( "-30T = -33060  =====>  T =  = 1102.\r\n" );
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document.write( "Thus,  1102 of the $10-tickets, 1102 + 182 = 1284 of the $20-tickets  and  3235-1102- 1284 = 849 of the $30-tickets were sold.\r\n" );
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document.write( "Check.  $10*1102 + $20*1284 + $30*849 = 62170.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Lesson to learn from this solution\r
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document.write( "    This problem is for one unknown, not for three.\r\n" );
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document.write( "    Your major task, when you start solve it, is to select the key unknown,\r\n" );
document.write( "    and then to express other quantities via that unknown.\r\n" );
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document.write( "    Then write the basic governing equation and solve it accurately.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The way @josgarithmetic tries to teach you is NOT THE WAY for solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "It is the way to NOWHERE.\r
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\n" ); document.write( "\n" ); document.write( "To see more similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - More solved word problems on a single linear equation\r
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\n" ); document.write( "Dear tutor @greenestamps !\r
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\n" ); document.write( "\n" ); document.write( "This problem is designed and assigned to 6-th or 7-th grade students, who did not study yet systems of equations and
\n" ); document.write( "DEFINITELY did not study systems of equations in three unknowns.\r
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