document.write( "Question 265878: Harry is twice as old as Sally was at the time when he was as old as Sally is now. Harry's age + Sally's age = 56 years. how old are they? \n" ); document.write( "

Algebra.Com's Answer #195426 by Edwin McCravy(20056) $\"\"$ $\"About$

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Harry is twice as old as Sally was at the time when he was as old as Sally is now. Harry's age + Sally's age = 56 years. how old are they?
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document.write( "Let H = Harry's age now.\r\n" );
document.write( "Let S = Sally's age now.\r\n" );
document.write( "Let x = the number of years ago talked about in the problem\r\n" );
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document.write( "The hard part is analyzing this sentence:\r\n" );
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document.write( "Harry is twice as old as Sally was \r\n" );
document.write( "at the time when he was as old as Sally is now.\r\n" );
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document.write( "That's quite a mouthfull.  Break that sentence down into two parts:\r\n" );
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document.write( "1.  Harry is twice as old as Sally was...\r\n" );
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document.write( "and \r\n" );
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document.write( "2.  ...at the time when he was as old as Sally is now.\r\n" );
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document.write( "To part 1 add the words \"x years ago\"\r\n" );
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document.write( "1.  Harry is twice as old as Sally was x years ago.\r\n" );
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document.write( "Change the words \"as old as Sally was x years ago\" to \"S-x\"\r\n" );
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document.write( "1.  Harry is twice S-x.\r\n" );
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document.write( "Now we can write the equation:\r\n" );
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document.write( "To part 2, which is\r\n" );
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document.write( "2.  ...at the time when he was as old as Sally is now.\r\n" );
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document.write( "change the words \"at the time when\" to \"x years ago\",\r\n" );
document.write( "and change \"he\" to \"Harry\" \r\n" );
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document.write( "2. x years ago, Harry was as old as Sally is now.\r\n" );
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document.write( "Change the words \"as old as Sally is now\" to \"S years old\"\r\n" );
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document.write( "2. x years ago, Harry was S years old.\r\n" );
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document.write( "So now we can write the equation\r\n" );
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document.write( "The last sentence\r\n" );
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document.write( "Harry's age + Sally's age = 56 years.\r\n" );
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document.write( "is easily changed to\r\n" );
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document.write( "So we have this system of three equations and 3 unknowns:\r\n" );
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document.write( "Rewrite the first equation\r\n" );
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document.write( "Rewrite the second equation\r\n" );
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document.write( "Now the system is\r\n" );
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document.write( "Can you solve that system of 3 equations in 3 unknowns?\r\n" );
document.write( "If not post again asking how.\r\n" );
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document.write( "Answers:  H=32, S=24, x=8.\r\n" );
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document.write( "Checking: \r\n" );
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document.write( "8 years ago Sally was 16, and Harry is now twice that, since he's 32.\r\n" );
document.write( "8 years ago Harry was 24, which is how old Sally is now, since she's 24.\r\n" );
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document.write( "That checks.\r\n" );
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document.write( "Edwin

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