document.write( "Question 1018857: A total of 50 tickets were sold for a play. Children tickets cost $5 and adult tickets cost $10. If the total sold was $350, how many tickets of each type were sold \n" ); document.write( "

Algebra.Com's Answer #634879 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Let the number of children's tickets be x\r\n" );
document.write( "Let the number of adult's tickets be y\r\n" );
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document.write( "                      Money      Money\r\n" );
document.write( "Type       Number     from       from\r\n" );
document.write( " of          of       EACH       ALL\r\n" );
document.write( "ticket    tickets    ticket     tickets\r\n" );
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document.write( "children    x           $5      $5x\r\n" );
document.write( "adults      y          $10     $10y\r\n" );
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document.write( "TOTALS     50        -----     $350\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 50\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "            5x + 10y = 350\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 50\r\n" );
document.write( "               y = 50 - x\r\n" );
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document.write( "Substitute (50 - x) for y in 5x + 10y = 350\r\n" );
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document.write( "  5x + 10(50 - x) = 350\r\n" );
document.write( "   5x + 500 - 10x = 350\r\n" );
document.write( "        -5x + 500 = 350\r\n" );
document.write( "              -5x = -150\r\n" );
document.write( "                x = 30 = the number of children's tickets.\r\n" );
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document.write( "Substitute in y = 50 - x\r\n" );
document.write( "              y = 50 - (30)\r\n" );
document.write( "              y = 20 adult tickets\r\n" );
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document.write( "Checking:  30 childrens is $150 and 20 adults is $200\r\n" );
document.write( "            That's 50 tickets.\r\n" );
document.write( "            And indeed $150 + $200 = $350\r\n" );
document.write( "Edwin

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