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A Little Algebra Anyone?

Can you solve this?

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#1 Uncle Hammer

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Posted 21 April 2007 - 11:58 PM

Hello all, I've been plagued with a rather what I find complicating algebra problem. So I'm deciding to throw it out here on the boards and see if one of you guys can tackle it. I know it has something to do with setting up a really long equation, but I get confused just reading the problem. Anyways here it is!


The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young.

How old is Old?
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#2 Rambo

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Posted 22 April 2007 - 12:29 AM

Bleh, too late, I could probably get it in the morning though.
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#3 DeceitfulSteve

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Posted 22 April 2007 - 05:25 AM

I started writing this method, gave up, tried guess-and-check, got the answer, google'd the question, and then rewrote my solution below. Besides guess and check, does anyone have a considerably easier solution? Also, let me know if some step doesn't make sense.

The ages of Old and Young total 48.

O + Y = 48
O = 48 - Y
Y = 48 - O
g = age gap = O - Y = O - (48 - O) = O - 48 + O = 2O - 48

Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as Old was when Old was three times as old as Young.

x = number of years since Old was three times as old as Young
>>Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as old as (O-x = 3(Y-x)).
Solve for x, to be used later:
O-x = 3(Y-x)
O-x = 3Y - 3x
48 - y - x = 3Y - 3x
48 + 2x = 4Y
x = 2Y-24

>>Old is twice as old as Young was when Old was half as old as 9(Y-x).


>>Old is twice as old as Young was when Old was (9(Y-x))/2.

>>Old is twice as old as (9(Y-x))/2 -g.

>>Old is 2((9(Y-x))/2 -g).
Replace x with 2Y-24, Y with 48 - O, and g with 2O - 48.
O = 9(Y-x) - 2g
O = 9(Y - 2Y + 24) - 2g = 9(24 - Y) -2g
O = 9(24 - (48 - O)) - 2g = 9(24 - 48 + O) - 2g = 9(O-24) - 2g
O = 9O - 216 - 2g
8O = 216 + 2g = 236 + 2(2O - 48) = 4O + 216 - 96
4O = 120
O = 30
Y = 18
>>Old is 30. Young is 18.

Q.E.D. ^_^
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#4 nerfboi

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Posted 22 April 2007 - 11:09 AM

Wow. I probabley could have done it, but when I looked at it last nihgt, I was like " nevermind, I'll do it in the morning." Nice job. And welcome to the boards?
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#5 Uncle Hammer

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Posted 22 April 2007 - 12:38 PM

Thank you kind sir. Ya I got about as far as old + young = 48 and then just reading the problem got me confused.
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Don't mess with Texas cuz its bigger than France, bitch..
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Catagory 5 hurricanes are the mighty dick of God.  You don't mess with that!  You don't mess with Gods dick!

#6 Rambo

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Posted 22 April 2007 - 12:49 PM

Guess I should've checked before I spent an hour trying to solve it...Nice job
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#7 taita cakes

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Posted 22 April 2007 - 08:55 PM

I prefer to add her to the bed.
Subtract her clothes.
Divide her legs.


And hope to god we don't multiply...
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#8 SHADOW HUNTER ALPHA

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Posted 22 April 2007 - 09:13 PM

Back on topic:

I used to get problems like this in my geometry / statistics class, but since that was last block I am kind of rusty on this material. Glad someone was able to post a thorough walkthrough of the problem.

Edited by SHADOW HUNTER ALPHA, 23 April 2007 - 09:37 PM.

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#9 Rambo

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Posted 22 April 2007 - 09:17 PM

That is older than the fucking Liberty Bell.
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#10 Mike

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Posted 23 April 2007 - 07:07 PM

I prefer to add her to the bed.
Subtract her clothes.
Divide her legs.


And hope to god we don't multiply...


Wow, that is the oldest and stupidest joke ever. That got old like 5 years ago, bud.
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#11 SHADOW HUNTER ALPHA

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Posted 23 April 2007 - 09:40 PM

Wow, that is the oldest and stupidest joke ever. That got old like 5 years ago, bud.


Believe me, shit travels SLOW in Delaware. Anyway, congrats to DS for having the only contributive and useful post in the thread so far.
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The only commonly shared fate among us all is death. I turn to the shadows so that I may not be unfamiliar with hell's corridors when I arrive. - SHADOW HUNTER ALPHA

Founder of the Shadow Militia.
Founder of Nightshade Laboratories and The Nightshade Armament Corporation.

#12 taita cakes

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Posted 24 April 2007 - 01:01 AM

Wow, that is the oldest and stupidest joke ever. That got old like 5 years ago, bud.


Point, please?
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#13 The Infinite Shindig

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Posted 24 April 2007 - 07:55 AM

There is no reason why anyone should be posting in this topic anymore.
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