document.write( "Question 862659: Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old as Grandma was when Grandpa was as old as Grandma is now. \n" ); document.write( "

Algebra.Com's Answer #854474 by ikleyn(53879) $\"\"$ $\"About$

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\n" ); document.write( "Together, Grandma and Grandpa are 140 years old. How old is Grandma if Grandpa was twice as old
\n" ); document.write( "as Grandma was when Grandpa was as old as Grandma is now.
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document.write( "Let P be the grandpa age (in years), and \r\n" );
document.write( "let M be the grandpa age.\r\n" );
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document.write( "First equation is\r\n" );
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document.write( "    P + M = 140.    (1)\r\n" );
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document.write( "When Grandpa was as old as Grandma ? - It happened (P-M) years ago.\r\n" );
document.write( "At that time, Grandma was M - (P-M) = 2M - P years old,\r\n" );
document.write( "while         Grandpa was P - (P-M) = M years old.\r\n" );
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document.write( "So, our second equation is\r\n" );
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document.write( "    M = 2(2M-P),  or  M = 4M - 2P,  which we transform to  2P = 3M.    (2).\r\n" );
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document.write( "So, we transform first equation (1) to\r\n" );
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document.write( "    2P + 2M = 280,\r\n" );
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document.write( "and then replace there 2P by 3M, based on (2).\r\n" );
document.write( "We get then\r\n" );
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document.write( "    3M + 2M = 280,\r\n" );
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document.write( "       5M   = 280,\r\n" );
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document.write( "        M   = 280/5 = 56.\r\n" );
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document.write( "At this point the solution is complete.\r\n" );
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document.write( "ANSWER.  Currently, grandma is 56 years old.\r\n" );
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