document.write( "Question 1102114: Tom is 2 years older than his brother. the product of their ages 6 years from now will be 120 more than the product of their present ages. Find each of their ages \n" ); document.write( "

Algebra.Com's Answer #716745 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The condition gives you two equations\r\n" );
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document.write( "T - B = 2,                  (1)\r\n" );
document.write( "(T+6)*(B+6) - T*B = 120.    (2)\r\n" );
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document.write( "Simplify eq(2):\r\n" );
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document.write( "T*B + 6B + 6T + 36 - T*B = 120,\r\n" );
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document.write( "6B + 6T = 120 - 36 = 84,\r\n" );
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document.write( "T + B =  = 14.\r\n" );
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document.write( "Thus the modified system of equation is THIS:\r\n" );
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document.write( "T - B =  2                   (3)\r\n" );
document.write( "T + B = 14                   (4)\r\n" );
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document.write( "Add the equations (3) and (4). You will get\r\n" );
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document.write( "2T = 2 + 14 = 16.   Hence,  T =  = 8.\r\n" );
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document.write( "Then from (4),  B = 14 - T = 14 - 8 = 6.\r\n" );
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document.write( "Answer.  Tom is 8 years old.  His brother is 6 years old.\r\n" );
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document.write( "Check.   (8+6)*(6+6) - 8*6 = 120.   ! Correct !\r\n" );
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