document.write( "Question 1106027: Jesse asks his math teacher her age and her husband's age. Jesse's teacher responds that it is not an appropriate question, but that she would use the opportunity to challenge Jesse with a riddle. She says, \"One third of my age is ten less than one half of my husband's age. The sum of our ages is 105.\" How old is Jesse's math teacher? \n" ); document.write( "

Algebra.Com's Answer #720944 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "So the problem is reduced to the solution of this system of 2 equations\r
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document.write( " =      (1)   (T = the teacher's age;  H = the husband's age)\r\n" );
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document.write( "T + H = 105.         (2)\r\n" );
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document.write( "First step is to multiply eq(1) by 6 (both sides) to simplify the system:\r\n" );
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document.write( "2T = 3H - 60         (1')\r\n" );
document.write( "T  + H = 105.        (2')\r\n" );
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document.write( "Next step is to express  H = 105 - T  from (2') and then to substitute it into eq(1') to get\r\n" );
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document.write( "2T = 3*(105-T) - 60,\r\n" );
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document.write( "2T = 315 - 3T - 60,\r\n" );
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document.write( "2T + 3T = 315 - 60  ====>  5T = 255.\r\n" );
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document.write( "And now YOU make the last step.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I used the Substitution method to solve the system for this problem.\r
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