document.write( "Question 1062300: Please help me. It's urgent. Question is \"When Bob was as old
\n" ); document.write( "as Rob was when Bob was half as old as Rob was when Bob was as
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\n" ); document.write( "was half as old as Bob is. One is in their teens. What are their
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Algebra.Com's Answer #677177 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You just had a period after the first phrase where you should \r\n" );
document.write( "have had a comma.\r\n" );
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document.write( "\"When Bob was as old as Rob was when Bob was half as old\r\n" );
document.write( "as Rob was when Bob was as old as Rob is, Rob was just a\r\n" );
document.write( "third as old as Bob was when Rob was half as old as Bob\r\n" );
document.write( "is. One is in their teens. What are their present ages?\"\r\n" );
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document.write( "Suppose Bob is B years old and Rob is R years old.\r\n" );
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document.write( "Look at just the first phrase:\r\n" );
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document.write( "When Bob was as old as Rob was when Bob was half as old\r\n" );
document.write( "as Rob was when Bob was as old as Rob is,\r\n" );
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document.write( "Let's translate these words on the end:\r\n" );
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document.write( "\"when Bob was as old as Rob is,\"\r\n" );
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document.write( "to a number of years ago.  Bob is older than Rob, so we\r\n" );
document.write( "subtract their ages, B-R to find out how many years ago\r\n" );
document.write( "that was.  So we rewrite the phrase as:\r\n" );
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document.write( "\"When Bob was as old as Rob was when Bob was half as old\r\n" );
document.write( "as Rob was B-R years ago.\"\r\n" );
document.write( "\r\n" );
document.write( "Let's translate these words on the end:\r\n" );
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document.write( "\"as old as Rob was B-R years ago.\"\r\n" );
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document.write( "to an age.  To find that, we subtract B-R years from\r\n" );
document.write( "Rob's age now, which is R and get\r\n" );
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document.write( "R-(B-R)\r\n" );
document.write( "R-B+R\r\n" );
document.write( "2R-B\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "\"When Bob was as old as Rob was when Bob was half of 2R-B\"\r\n" );
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document.write( "Let's translate the words on the end:\r\n" );
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document.write( "\"half of 2R-B\"\r\n" );
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document.write( "to an age as \r\n" );
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document.write( "\"expr%281%2F2%29%282R-B%29\"\r\n" );
document.write( "\"R-expr%281%2F2%29B\" years old\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "\"When Bob was as old as Rob was when Bob was \"R-expr%281%2F2%29B\"\r\n" );
document.write( "years old.\"\r\n" );
document.write( "\r\n" );
document.write( "Let's translate the words on the end:\r\n" );
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document.write( "\"when Bob was \"R-expr%281%2F2%29B\" years old\"\r\n" );
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document.write( "to a number of years ago.  To find how many years ago\r\n" );
document.write( "that was, we subtract \"R-expr%281%2F2%29B\"\" from Bob's age now, \r\n" );
document.write( "which is B:\r\n" );
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document.write( "\"B-%28R-expr%281%2F2%29B%29\"\r\n" );
document.write( "\"B-R%2Bexpr%281%2F2%29B\"\r\n" );
document.write( "\"expr%283%2F2%29B-R\" years ago.\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "\"When Bob was as old as Rob was \"expr%283%2F2%29B-R%29\" years ago.\r\n" );
document.write( "\r\n" );
document.write( "Let's translate the words on the end:\r\n" );
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document.write( "\"as old as Rob was \"expr%283%2F2%29B-R%29\" years ago.\"\r\n" );
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document.write( "We subtract that from Rob's age now:\r\n" );
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document.write( "\"R-%28expr%283%2F2%29B-R%29\"\r\n" );
document.write( "\"R-expr%283%2F2%29B%2BR\"\r\n" );
document.write( "\"2R-expr%283%2F2%29B\"\r\n" );
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document.write( "So now we have\r\n" );
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document.write( "\"When Bob was \"2R-expr%283%2F2%29B\" years old.\"\r\n" );
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document.write( "We translate that to a number of years ago by subtracting\r\n" );
document.write( "it from B:\r\n" );
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document.write( "\"B-%282R-expr%283%2F2%29B%29\"\r\n" );
document.write( "\"B-2R%2Bexpr%283%2F2%29B\"\r\n" );
document.write( "\"expr%285%2F2%29B-2R\" years ago.\r\n" );
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document.write( "Now we look at the second phrase:\r\n" );
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document.write( "\"Rob was just a third as old as Bob was when Rob was half\r\n" );
document.write( "as old as Bob is\"\r\n" );
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document.write( "Notice the first two words:\r\n" );
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document.write( "\"Rob was\".\r\n" );
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document.write( "Let's replace that by Rob's age \"expr%285%2F2%29B-2R\" years ago.  We do that by subtracting it from Rob's age now,\r\n" );
document.write( "which is R:\r\n" );
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document.write( "\"R-%28expr%285%2F2%29B-2R%29\"\r\n" );
document.write( "\"R-expr%285%2F2%29B%2B2R\"\r\n" );
document.write( "\"3R-expr%285%2F2%29B\"\r\n" );
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document.write( "and put an = sign after it because that is the subject of\r\n" );
document.write( "the second phrase:\r\n" );
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document.write( "\"\"3R-expr%285%2F2%29B\"\"%22%22=%22%22\" just a third as old as Bob was when \r\n" );
document.write( "Rob was half as old as Bob is\"\r\n" );
document.write( "\r\n" );
document.write( "Let's translate the words on the end:\r\n" );
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document.write( "\"half as old as Bob is\"\r\n" );
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document.write( "That's simply \"expr%281%2F2%29B\" years old.\r\n" );
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document.write( "So now we have:\r\n" );
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document.write( "\"\"3R-expr%285%2F2%29B\"\"%22%22=%22%22\" just a third as old as Bob was when Rob \r\n" );
document.write( "was \"expr%281%2F2%29B\" years old.\"\r\n" );
document.write( "\r\n" );
document.write( "Let's translate the words on the end:\r\n" );
document.write( "\r\n" );
document.write( "\"when Rob was \"expr%281%2F2%29B\" years old.\"\r\n" );
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document.write( "to a number of years ago.  We do that by subtracting \"expr%281%2F2%29B\" \r\n" );
document.write( "years from Rob's age now, which is R:\r\n" );
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document.write( "\"R-expr%281%2F2%29B\" years ago.\r\n" );
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document.write( "So now we have:\r\n" );
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document.write( "\"\"3R-expr%285%2F2%29B\"\"%22%22=%22%22\" just a third as old as Bob was \r\n" );
document.write( "\"R-expr%281%2F2%29B\" years ago.\"\r\n" );
document.write( "\r\n" );
document.write( "Let's translate the words on the end:\r\n" );
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document.write( "\"as old as Bob was \"R-expr%281%2F2%29B\" years ago\"\r\n" );
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document.write( "to the age of Bob then.  We do that by subtracting \"R-expr%281%2F2%29B\" \r\n" );
document.write( "from Bob's age now, which is B:\r\n" );
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document.write( "\"B-%28R-expr%281%2F2%29B%29\"\r\n" );
document.write( "\"B-R%2Bexpr%281%2F2%29B\"\r\n" );
document.write( "\"expr%283%2F2%29B+-+R\"\r\n" );
document.write( " \r\n" );
document.write( "So now we have:\r\n" );
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document.write( "\"3R-expr%285%2F2%29B\"\"%22%22=%22%22\" just a third (of) \"expr%283%2F2%29B+-+R\"\r\n" );
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document.write( "So we just put \"1%2F3\" in front of that:\r\n" );
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document.write( "\"3R-expr%285%2F2%29B\"\"%22%22=%22%22\"\"expr%281%2F3%29%28expr%283%2F2%29B+-+R%29\"\r\n" );
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document.write( "Multiply both sides by 6\r\n" );
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document.write( "\"18R-15B\"\"%22%22=%22%22\"\"2%28expr%283%2F2%29B+-+R%29\"\r\n" );
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document.write( "\"18R-15B\"\"%22%22=%22%22\"\"3B+-+2R%29\"\r\n" );
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document.write( "\"20R\"\"%22%22=%22%22\"\"18B\"\r\n" );
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document.write( "That simplifies to\r\n" );
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document.write( "\"9B\"\"%22%22=%22%22\"\"10R\"\r\n" );
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document.write( "\"B\"\"%22%22=%22%22\"\"expr%2810%2F9%29R\"\r\n" );
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document.write( "So R must be divisible by 9,\r\n" );
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document.write( " So R =  9, 18, 27, 36, 45, 54, 63, 72, 81, 90,...\r\n" );
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document.write( "And B = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,... \r\n" );
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document.write( "Now we use this sentence:\r\n" );
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document.write( "\"One is in their teens.\"\r\n" );
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document.write( "There is only one possibility,\r\n" );
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document.write( "Rob is 18 and Bob is 20.\r\n" );
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document.write( "Edwin
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