document.write( "Question 1143483: Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 92. Two adults and three children must pay $65. Find the price of the adult's ticket and the price of a child's ticket. \n" ); document.write( "

Algebra.Com's Answer #764292 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "    3a + 4c = 92    (1)\r\n" );
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document.write( "    2a + 3c = 65    (2)\r\n" );
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document.write( "To solve it, multiply eq(1) by 2 and multiply eq(2) by 3.  You will get\r\n" );
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document.write( "    6a + 8c = 2*92     (1')\r\n" );
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document.write( "    6a + 9c = 3*65     (2')\r\n" );
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document.write( "Now subtract eq(1') from eq(2').  You will get\r\n" );
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document.write( "    c  = 3*65 - 2*92 = 11.\r\n" );
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document.write( "To find \"a\", substitute  c= 11 into equation (1)\r\n" );
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document.write( "    3a + 4*11 = 92\r\n" );
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document.write( "    3a = 92 - 44\r\n" );
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document.write( "    3a = 48\r\n" );
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document.write( "     a = 48/3 = 16.\r\n" );
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document.write( "ANSWER.  Adult's ticket price is $16;  child's ticket price is $11.\r\n" );
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