Age problem

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DJ_PAPA
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Age problem

Postby DJ_PAPA » Sat Apr 25, 2009 1:45 am UTC

The grand-father of Joe has 7 times the age that Joe had 6 years ago.
In 26 years he (the grand-father) will will have only 5 times his age. How many years Joe has?

It's better from people to put here the way that each one used to get the answer :P

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eaglef2
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Re: Age problem

Postby eaglef2 » Sat Apr 25, 2009 2:01 am UTC

your question is posed poorly, by 26 years do you mean 26 years from 6 years ago or 26 years from his current age, not to mention that your numbers break the record for oldest man for the grandfather, if you start at Joe's final age being just 26, then his grandfather will have to be 130 years old in order to have 5x the age.

You need to rethink this question

but I worked out this problem using algebra:
Spoiler:
so we know the grandfather's age, GA, to be 7x greater than Joe's age, JA, six years ago, so GA - 6 = 7(JA - 6). and in 26 years of 6 years ago GA + 20 = 5(JA + 20) so using algebra you get 2JA = 116 and JA = 58, so Joe is 58 years old right now and his grandfather is 290 years old

using 26 years from now you get that GA + 26 = 5(JA + 26) and GA - 6 = 7(JA - 6) so JA = 70, meaning that his grandfather is 350 years old
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quintopia
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Re: Age problem

Postby quintopia » Sat Apr 25, 2009 4:58 am UTC

If you adopt the convention that, until someone is born, their age is and has always been zero, then Joe is not born yet is also a valid solution.

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eaglef2
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Re: Age problem

Postby eaglef2 » Sat Apr 25, 2009 5:40 am UTC

that also means that his grandfather could not have been born yet however. For example if Joe is 6 then his age six years ago would be 0, and 0 * 7 = 0; a way this could be possible is time travel like Phillip J. Fry.
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6453893
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Re: Age problem

Postby 6453893 » Sat Apr 25, 2009 8:20 am UTC

I parsed the question as closely to what the OP said as I could. But it is fairly unclear.

Spoiler:
G=7(J-6)

G+26=5(J+26)

7(J-6)+26=5(J+26)

J=73

G=7(73-6)

G=469

So J is 73 right now, and the Grandfather is 469. Yeah, great question.

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jestingrabbit
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Re: Age problem

Postby jestingrabbit » Sat Apr 25, 2009 10:25 am UTC

I gotta say that this looks more than a little like homework. Please show your working?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

DJ_PAPA
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Re: Age problem

Postby DJ_PAPA » Sat Apr 25, 2009 5:57 pm UTC

Spoiler:
x = 7*(y-6) <=> x = 7y - 42

x + 26 = 5* (y+26) <=> 7y - 42 + 26 = 5y + 130 <=> 2y = 130 +16 <=> y = 73

x = 7y - 42 <=> x = 7*73 - 42 <=> x = 469

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jestingrabbit
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Re: Age problem

Postby jestingrabbit » Sat Apr 25, 2009 6:01 pm UTC

Looks like a question that yields crazy numbers for answers.

In the future if something is homework please mention it.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

DJ_PAPA
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Re: Age problem

Postby DJ_PAPA » Sat Apr 25, 2009 6:09 pm UTC

No Homework :wink:

There is also the confirmation part:
Spoiler:
(X - Y) = constant anywhere in time
(73 - 469) = (99 - 495 )

Also:
(73-6)= 67 and 67*7=469
469+26=495 and 495/5=99 = 73+26

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6453893
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Re: Age problem

Postby 6453893 » Sun Apr 26, 2009 6:52 am UTC

I have one. Fifty years ago Bob's Grandfather was nine times his age. In fifty years Bob's Grandfather will be 13 times his age. How old is Bob now? Please show all working.

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eaglef2
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Re: Age problem

Postby eaglef2 » Sun Apr 26, 2009 9:19 am UTC

You present an impossibility in limits. as Bob's age and his grandfather's ages go to infinite, the ratio of the two ages approach one. For example, a 21 year old man says to his friend that this 7 year old girl will be his wife one day. Disgusted his friend says, "but you are three times her age!" He responds, "Yes, but in seven years I will only be twice her age, and in another seven years I'll only be 5/3 her age." As you can see the ratio of increasing ages always approaches one, not infinite.
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Entropy
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Re: Age problem

Postby Entropy » Sun Apr 26, 2009 11:12 am UTC

Perhaps, but you have neglected the fact that Bob likes to travel in a space ship which goes nearly the speed of light. ;)

Spoiler:
That, or Bob will be born 250 years from now, a mere 2400 years before his grandfather.

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eaglef2
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Re: Age problem

Postby eaglef2 » Sun Apr 26, 2009 7:00 pm UTC

Yeah relativity caught me, however, if his grandfather were to also like doing that, except in the exact opposite direction, I wonder how interesting that would be.
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-Azula, Avatar: The Last Airbender.

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airplanespaceship3
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Re: Age problem

Postby airplanespaceship3 » Sun Apr 26, 2009 8:39 pm UTC

Bob died at the tender age of 25. ;_'
I guess his grandfather has better life support systems. @_@
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6453893
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Re: Age problem

Postby 6453893 » Mon Apr 27, 2009 2:06 pm UTC

eaglef2 wrote:You present an impossibility in limits.


But, you did not take into account that I had to make the answer more ridiculous than the OPs. If you had, you would have clearly found that

Spoiler:
Bob is negative two-hundred-and-seventy-something years old, while his grandfather is in the negative 2900's.

itaibn
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Re: Age problem

Postby itaibn » Fri May 29, 2009 8:53 pm UTC

6453893 wrote:But, you did not take into account that I had to make the answer more ridiculous than the OPs. If you had, you would have clearly found that

Spoiler:
Bob is negative two-hundred-and-seventy-something years old, while his grandfather is in the negative 2900's.
I doesn't have to be that ridiculous:
Spoiler:
Bob could be 65286 years old while his grandfather is 62886 years old. See http://xkcd.com/571/.
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