document.write( "Question 447411: Tom is twice as old as Dick was when Harry was one year younger than Tom is now.
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\n" ); document.write( "Harry is one and a half times as old as Tom was when Dick was ten years younger than Harry is now. how old are Tom, Dick, and Harry? \n" ); document.write( "

Algebra.Com's Answer #308077 by Edwin McCravy(20056) $\"\"$ $\"About$

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Tom is twice as old as Dick was when Harry was one year younger than Tom is now.
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document.write( "Let x = the number of years ago it was when Harry was a year \r\n" );
document.write( "younger than Tom is now.\r\n" );
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document.write( "Then\r\n" );
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document.write( "h-x = t-1 \r\n" );
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document.write( "Dick was d-x then.\r\n" );
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document.write( "And Tom is twice that age now, so\r\n" );
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document.write( "t = 2(d-x)\r\n" );
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document.write( "t = 2d-2x\r\n" );
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document.write( "Dick is half as old as Harry will be when Tom is ten years \r\n" );
document.write( "older than Dick is now.\r\n" );
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document.write( "Let y be the number of years when Tom is ten years older \r\n" );
document.write( "than Dick is now.\r\n" );
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document.write( "Then \r\n" );
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document.write( "t+y = d+10\r\n" );
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document.write( "Then in y years Harry will be h+y and Dick's age is half \r\n" );
document.write( "of that, so\r\n" );
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document.write( "d = (h+y)/2 or clear of fractions:\r\n" );
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document.write( "2d = h+y\r\n" );
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document.write( "Harry is one and a half times as old as Tom was when Dick \r\n" );
document.write( "was ten years younger than Harry is now. \r\n" );
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document.write( "Let z = the number of years since Dick was ten years \r\n" );
document.write( "younger than Harry is now.\r\n" );
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document.write( "Then\r\n" );
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document.write( "d-z = h-10\r\n" );
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document.write( "Tom was t-z\r\n" );
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document.write( "Harry is 1.5 times that.  So\r\n" );
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document.write( "h = 1.5(t-z)\r\n" );
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document.write( "or multiplying both sides by 2 to avoid fractions\r\n" );
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document.write( "2h = 3(t-z)\r\n" );
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document.write( "And distributing to avoid parentheses:\r\n" );
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document.write( "2h = 3t-3z\r\n" );
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document.write( "We have this system of 6 equations in 6 unknowns\r\n" );
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document.write( "h-x = t-1\r\n" );
document.write( "t = 2d-2x  \r\n" );
document.write( "t+y = d+10\r\n" );
document.write( "2d = h+y\r\n" );
document.write( "d-z = h-10\r\n" );
document.write( "2h = 3t-3z\r\n" );
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document.write( "Solve that either by subtitution or elimination\r\n" );
document.write( "and get\r\n" );
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document.write( "t=18, d=16, h=24, x=7, y=8, z=2 \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Tom is twice as old as Dick was when Harry was one year \r\n" );
document.write( "younger than Tom is now.\r\n" );
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document.write( "Tom is 18. 7 years ago Harry was 17, which is 1 year \r\n" );
document.write( "younger than Tom is now. And 7 years ago Dick was 9, \r\n" );
document.write( "and Tom is indeed twice that. \r\n" );
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document.write( "Dick is half as old as Harry will be when Tom is ten \r\n" );
document.write( "years older than Dick is now.\r\n" );
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document.write( "In 8 years, Tom will be 26, and will indeed be 10 years \r\n" );
document.write( "older than Dick is now. \r\n" );
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document.write( "In 8 years, Harry will be 32, and indeed Dick is half \r\n" );
document.write( "that now.\r\n" );
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document.write( "Harry is one and a half times as old as Tom was when \r\n" );
document.write( "Dick was ten years younger than Harry is now.\r\n" );
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document.write( "2 years ago Dick was 14 and that is 10 years younger \r\n" );
document.write( "than Harry's present age of 24.\r\n" );
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document.write( "2 years ago Tom was 16 and Harry is 1.5 times that or 24.\r\n" );
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document.write( "So everything checks.\r\n" );
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document.write( "Edwin

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