## Age problem

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DJ_PAPA
Posts: 3
Joined: Sat Apr 25, 2009 1:38 am UTC

### Age problem

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

eaglef2
Posts: 93
Joined: Mon Feb 09, 2009 4:52 am UTC
Location: I am over there

### Re: Age problem

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
"I am a four hundred-foot tall purple Platypus Bear with pink horns and silver wings."
-Azula, Avatar: The Last Airbender.

quintopia
Posts: 2906
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Location: atlanta, ga

### Re: Age problem

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.

eaglef2
Posts: 93
Joined: Mon Feb 09, 2009 4:52 am UTC
Location: I am over there

### Re: Age problem

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.
"I am a four hundred-foot tall purple Platypus Bear with pink horns and silver wings."
-Azula, Avatar: The Last Airbender.

6453893
Posts: 557
Joined: Wed Dec 13, 2006 2:40 am UTC
Location: Australia

### Re: Age problem

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.

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
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Location: Sydney

### Re: Age problem

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
Posts: 3
Joined: Sat Apr 25, 2009 1:38 am UTC

### Re: Age problem

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

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: Age problem

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
Posts: 3
Joined: Sat Apr 25, 2009 1:38 am UTC

### Re: Age problem

No Homework

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

6453893
Posts: 557
Joined: Wed Dec 13, 2006 2:40 am UTC
Location: Australia

### Re: Age problem

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.

eaglef2
Posts: 93
Joined: Mon Feb 09, 2009 4:52 am UTC
Location: I am over there

### Re: Age problem

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.
"I am a four hundred-foot tall purple Platypus Bear with pink horns and silver wings."
-Azula, Avatar: The Last Airbender.

Entropy
Posts: 233
Joined: Sun Apr 20, 2008 9:40 pm UTC

### Re: Age problem

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.

eaglef2
Posts: 93
Joined: Mon Feb 09, 2009 4:52 am UTC
Location: I am over there

### Re: Age problem

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.
"I am a four hundred-foot tall purple Platypus Bear with pink horns and silver wings."
-Azula, Avatar: The Last Airbender.

airplanespaceship3
Posts: 16
Joined: Tue Apr 21, 2009 6:04 am UTC
Location: Southern California
Contact:

### Re: Age problem

Bob died at the tender age of 25. ;_'
I guess his grandfather has better life support systems. @_@
"What's 2+2?"
"What do you want it to be?"

6453893
Posts: 557
Joined: Wed Dec 13, 2006 2:40 am UTC
Location: Australia

### Re: Age problem

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
Posts: 142
Joined: Mon Dec 29, 2008 7:06 pm UTC

### Re: Age problem

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/.
I NEVER use all-caps.