document.write( "Question 365530: Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter? \n" ); document.write( "
Algebra.Com's Answer #260589 by Edwin McCravy(20055)\"\" \"About 
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Peter and Paul are two friends. The sum of their ages is 35 years. Peter is twice as old as Paul was when Peter was as old as Paul is now. What is the present age of Peter?
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document.write( "Let x = Peter's present age\r\n" );
document.write( "Let y = Paul's present age\r\n" );
document.write( "Let z = the number of years ago indicated by the word \"when\" above.\r\n" );
document.write( "x - z = Peter's age z years ago\r\n" );
document.write( "y - z = Paul's age z years ago\r\n" );
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\n" ); document.write( ">>The sum of their ages is 35 years.<<
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document.write( "So x + y = 35
>>Peter is twice as old as Paul was when Peter was as old as Paul is now.<<
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document.write( "We first need to express how old Paul was when Peter was as old as Paul is now.\r\n" );
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document.write( "That was z years ago, so z years ago, Peter was x - z, and that is the age Paul\r\n" );
document.write( "is now, so\r\n" );
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document.write( "x - z = y\r\n" );
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document.write( "But Paul was y - z then \r\n" );
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document.write( "We are told that Peter is now twice that (Paul's age then), so\r\n" );
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document.write( "x = 2(y - z) \r\n" );
document.write( "x = 2y - 2z\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "x + y = 35\r\n" );
document.write( "x - z = y\r\n" );
document.write( "x = 2y - 2z\r\n" );
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document.write( "Lining them up makes the system easier to solve:\r\n" );
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document.write( "x +  y      = 35\r\n" );
document.write( "x -  y -  z =  0\r\n" );
document.write( "x - 2y + 2z =  0\r\n" );
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document.write( "I assume you can solve that.  If not post again asking how.\r\n" );
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document.write( "Solution:  x=20, y=15, z=5\r\n" );
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document.write( "So Peter is 20, Paul is 15, and the number of years ago is 5\r\n" );
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document.write( "You were only asked for Peter's age, so the answer is 20.\r\n" );
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document.write( "Let's check with the words:\r\n" );
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document.write( "The sum of their ages is 35 years. \r\n" );
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document.write( "That checks because 20 + 15 = 35 \r\n" );
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document.write( "Peter is twice as old as Paul was when Peter was as old as Paul is now. \r\n" );
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document.write( "Now it has been 5 years since Peter was as old as Paul is now, for 5 years ago\r\n" );
document.write( "Peter was 15 and that's how old Paul is now.  But 5 years ago Paul was 10, and\r\n" );
document.write( "so Peter, who is now 20, is now twice as old as Paul was then.\r\n" );
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document.write( "Edwin

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