document.write( "Question 1026490: If 108 attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.75 and total receipts for the concert was $351.75, how many of each went to the concert? \n" ); document.write( "

Algebra.Com's Answer #641793 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Let the number of adults' tickets be x\r\n" );
document.write( "Let the number of children'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" );
document.write( "-------------------------------------------\r\n" );
document.write( "adult's        x      $3.50      $3.50x\r\n" );
document.write( "children's     y      $2.75      $2.75y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       108      -----      $351.75\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" );
document.write( "                 x + y = 108\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \r\n" );
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document.write( "           3.50x + 2.75y = 351.75\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 100:\r\n" );
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document.write( "             350x + 275y = 35175\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 = 108\r\n" );
document.write( "                       y = 108 - x\r\n" );
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document.write( "Substitute (108 - x) for y in 350x + 275y = 35175\r\n" );
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document.write( "     350x + 275(108 - x) = 35175\r\n" );
document.write( "     350x + 29700 - 275x = 35175\r\n" );
document.write( "             75x + 29700 = 35175\r\n" );
document.write( "                     75x = 5475\r\n" );
document.write( "                       x = 73 = the number of adult tickets.\r\n" );
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document.write( "Substitute in          y = 108 - x\r\n" );
document.write( "                       y = 108 - (73)\r\n" );
document.write( "                       y = 35 children's tickets.\r\n" );
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document.write( "Checking:  73 adults' is $255.50 and 35 children's is $96.25\r\n" );
document.write( "            That's 108 tickets.\r\n" );
document.write( "            And indeed $255.50 + $96.25 = $351.75\r\n" );
document.write( "Edwin

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