document.write( "Question 1205573: Hi
\n" ); document.write( "Alex says to Sarah when I was as old as you today the sum of our ages was 27 years. Sarah replied when I will be as old as you are today the sum of our ages will be 55 years.
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Algebra.Com's Answer #842469 by ikleyn(52914) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Alex says to Sarah when I was as old as you today the sum of our ages was 27 years.
\n" ); document.write( "Sarah replied when I will be as old as you are today the sum of our ages will be 55 years.
\n" ); document.write( "How old $\"highlight%28cross%28are%29%29\"$ is each of them.
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document.write( "Let A be the Alex's age;  S be the Sarah's age.\r\n" );
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document.write( "First sentence \"Alex says to Sarah when I was as old as you today the sum of our ages was 27 years\"\r\n" );
document.write( "is translated to this equation\r\n" );
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document.write( "    [A - (A-S)] + [S - (A-S)] = 27    (it happened A-S years ago).\r\n" );
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document.write( "This equation is equivalent to\r\n" );
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document.write( "    S + 2S - A = 27,   or   3S - A = 27.    (1)\r\n" );
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document.write( "Second sentence \"Sarah replied when I will be as old as you are today the sum of our ages will be 55 years\"\r\n" );
document.write( "is translated to this equation\r\n" );
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document.write( "    [S + (A-S)] + [A + (A-S)] = 55    (it will happen in A-S years).\r\n" );
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document.write( "This equation is equivalent to\r\n" );
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document.write( "    A + A + A - S = 55,   or   3A -S = 55.    (2).\r\n" );
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document.write( "So, we have the system of two equations (1) and (2).\r\n" );
document.write( "To solve it, from equation (1) express A = 3S - 27  and substitute it into equation (2).\r\n" );
document.write( "You will get\r\n" );
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document.write( "    3*(3S-27) - S = 55,\r\n" );
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document.write( "    9S - 81 - S = 55,\r\n" );
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document.write( "    9S - S = 55 + 81\r\n" );
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document.write( "       8S  =   136\r\n" );
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document.write( "        S  =   136/8 = 17.\r\n" );
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document.write( "Then A = 3S - 27 = 3*17 - 27 = 24.\r\n" );
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document.write( "ANSWER.  Alex is 24 years old;  Sarah is 17 years old.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The solution by Theo is incorrect, since his setup equations are incorrect.\r
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