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Duane
 Senior Boarder
Posts: 63 
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Here is a problem by J.A.H. Hunter.
Bert was finding life rather lonely-in town only a few weeks. He still knew nobody outside of the small office. 'How old is that kid sister of yours?' he asked Ben as they ate their lunch in the cafeteria. 'Still too young for you' laughed Ben, 'but maybe you can wait 11 years.' Bert grinned. 'Why 11? What happens then'. Ben was ready for that question. 'If you multiply my age by the difference between seven times Pam's age and three times mine you'll get the age she will be then.' He smiled at the surprised look on the othe man's face. 'And all ages without fractions of years, of course'. Bert didn't even try to figure it out, he didn't feel that way about figures. But what do you make Pam's age?
Please give the answer with the method to get the answer or if there is no answer prove it.
Peter Heichelheim
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Jaxler
 Senior Boarder
Posts: 67
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answer in spoiler space below
keep going../
keep going....
almost there..
Pam = 8 , 19 in 11 years ,,me 19 now
Check 3*19 - 7*8 = 1,,,,,,1*19 =19
Method: ( Standard ) M(7P-3M) = P +11 Gives quadratic with parameter P Use quadratic Formula Trial and error between 5 and up Make spreadsheet.
Method 2. Make 2-D spreadsheet with self referential implicit formula above.
Method 3. Is this a Diophantine again??
RJ Pease
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myrrrffs
 Expert Boarder
Posts: 90
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Very good. You got J.A.H. Hunter's answer which was Pam was 8 years old.
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glundby
Expert Boarder
Posts: 81
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Hmm, my quadratic solution went wrong, can someone point out the (obvious?) error
M(7P-3M) = P +11
7PM - 3M^2 = P+11
3M^2 - 7PM + P+11 = 0
(where ^2 is to the power 2)
so quadratic solution is
M =mm, my quadratic solution went wrong, can someone point out the (obvious?) error
M(7P-3M) = P +11
7PM - 3M^2 = P+11
3M^2 - 7PM + P+11 = 0
(where ^2 is to the power 2)
so quadratic solution is
M =[ 7P +- sqrt(49P^2 - 12(P+11)) ]/ 6
?
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Johnders
Expert Boarder
Posts: 88
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There's an ambiguity in the phrase 'the difference between seven times Pam's age and three times mine'
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johngnova
Senior Boarder
Posts: 75
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I see now, thanks. I should have seen that in the first place. I'm relieved that my maths hasn't degraded though.
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mintgus
Senior Boarder
Posts: 76
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It's not solvable with the information given. And who the heck is this Pam person, anyway?
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johngnova
Senior Boarder
Posts: 75
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It's solvable because the ages have to be positive integers.
Diophantine Equations or trial and error. answer is 8
RJ Pease
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Mirelo
Senior Boarder
Posts: 76
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There is nothing wring with the maths, but I think you missed my point. Does it explicitly state that Pam is the Sister?
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Linda2
Senior Boarder
Posts: 64
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What color was the bear?
RJ P
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