document.write( "Question 139458: The age of three grand oaks totals exactly one thousand years. From the following information, determine the age of each tree. When the youngest tree has reached the age of the middle tree, the middle tree will be the age of the oldest tree and four times the current age of the youngest tree. Please help me solve this...I don't know what to do! \n" ); document.write( "
Algebra.Com's Answer #101762 by Edwin McCravy(20059)\"\" \"About 
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The age of three grand oaks totals exactly one thousand years. From the following information, determine the age of each tree. When the youngest tree has reached the current age of the middle tree, the middle tree will be the current age of the eldest tree and four times the current age of the youngest tree. Please help me solve this...I don't know what to do!
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document.write( "Let Y = the age of the youngest tree\r\n" );
document.write( "Let M = the age of the middle tree\r\n" );
document.write( "Let E = the age of the ELDEST tree.  \r\n" );
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document.write( ">>...The age of three grand oaks totals exactly one thousand years...<<\r\n" );
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document.write( "So\r\n" );
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document.write( "Y + M + E = 1000\r\n" );
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document.write( "That's the first equation.\r\n" );
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document.write( ">>...When the youngest tree has reached the age of the middle tree,...<<\r\n" );
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document.write( "The difference between the youngest and middle tree is M - Y\r\n" );
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document.write( "So M-Y is how many years will have passed when the youngest tree has \r\n" );
document.write( "reached the present age of the middle tree.\r\n" );
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document.write( ">>... the middle tree will be the age of the oldest tree...<<\r\n" );
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document.write( "So after those M-Y years, the middle tree will be E, the age of the \r\n" );
document.write( "Eldest.\r\n" );
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document.write( "So when we add M-Y to the middle tree's age, M, we get E.  Therefore\r\n" );
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document.write( "  M + (M-Y) = E     \r\n" );
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document.write( "That's the second equation.\r\n" );
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document.write( ">>...When the youngest tree has reached the age of the middle tree, \r\n" );
document.write( "the middle tree will be...four times the current age of the youngest \r\n" );
document.write( "tree...<<\r\n" );
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document.write( " M + (M-Y) = 4Y\r\n" );
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document.write( "That's the third equation.\r\n" );
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document.write( "So we have this system of three equations in three unknowns\r\n" );
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document.write( " Y + M + E = 1000\r\n" );
document.write( " M + (M-Y) = E\r\n" );
document.write( " M + (M-Y) = 4Y\r\n" );
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document.write( "which simplies to\r\n" );
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document.write( " Y +  M + E = 1000\r\n" );
document.write( "-Y + 2M - E = 0\r\n" );
document.write( "-5 + 2M     = 0\r\n" );
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document.write( "I assume you can solve that system of equation.\r\n" );
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document.write( "Solution: Y = 133\"1%2F3\" years\r\n" );
document.write( "          M = 333\"1%2F3\" years\r\n" );
document.write( "          E = 533\"1%2F3\" years\r\n" );
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document.write( "--------------------------------------------\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The age of three grand oaks totals exactly one thousand years. \r\n" );
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document.write( "133\"1%2F3\" + 333\"1%2F3\" + 533\"1%2F3\" = 1000\r\n" );
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document.write( "That checks.\r\n" );
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document.write( ">>...When the youngest tree has reached the age of the middle tree,...<<\r\n" );
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document.write( "That will take 200 years.\r\n" );
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document.write( ">>... the middle tree will be the age of the oldest tree...<<\r\n" );
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document.write( "That checks, because the eldest tree is 200 years older than the \r\n" );
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document.write( ">>...and four times the current age of the youngest tree...<<\r\n" );
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document.write( "That checks because 4 times 133\"1%2F3\" is 533\"1%2F3\".\r\n" );
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document.write( "Edwin
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