document.write( "Question 69389: Marie is one-ninth as old as her mother. In three years, she will be one-fourth as old as her mother will be then. Find their present ages. \n" ); document.write( "

Algebra.Com's Answer #49400 by Edwin McCravy(20055) $\"\"$ $\"About$

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Marie is one-ninth as old as her mother.  In three years,\r\n" );
document.write( "she will be one-forth as old as her mother will be then.  \r\n" );
document.write( "Find their present ages.  \r\n" );
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document.write( "Rewrite it without fractions:\r\n" );
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document.write( "Marie's mother is 9 times as old as Marie is..  In three years, her\r\n" );
document.write( "mother will be 4 times as old as Marie will be then.  \r\n" );
document.write( "Find their present ages. \r\n" );
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document.write( "Let Marie's age be x\r\n" );
document.write( "Then Marie's mother's age is 9x\r\n" );
document.write( "Marie's age in 3 years will be x + 3\r\n" );
document.write( "Marie's mother's age in 3 years will be 9x + 3\r\n" );
document.write( "Marie's mother's age in 3 years will also be 4(x + 3)\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "9x + 3 = 4(x + 3)\r\n" );
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document.write( "9x + 3 = 4x + 12\r\n" );
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document.write( "5x = 9 \r\n" );
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document.write( "x = 1.8 years and her mother is 16.2\r\n" );
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document.write( "That checks because:\r\n" );
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document.write( "Marie (who is 1.8 years old) is one-ninth as old as her mother, who is 16.2)\r\n" );
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document.write( "That checks because 1/9 of 16.2 is 1.8 \r\n" );
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document.write( "In three years, she will be 4.8, and mother will be 19.2  \r\n" );
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document.write( "That checks because 1/4 of 19.2  is 4.8.\r\n" );
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document.write( "So Marie is 1.8 years old and her mother is 16.2 years old.\r\n" );
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document.write( "I guess there have been mothers who had a baby when they were \r\n" );
document.write( "14.4 years old, but this is hopefully a rare occurrence.\r\n" );
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document.write( "Edwin

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