12 replies to this topic

[Uncle Hammer]

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?

[Rambo]

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

[DeceitfulSteve]

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.

[nerfboi]

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?

[Uncle Hammer]

Thank you kind sir. Ya I got about as far as old + young = 48 and then just reading the problem got me confused.

[Rambo]

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

[taita cakes]

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


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

[SHADOW HUNTER ALPHA]

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.

[Rambo]

That is older than the fucking Liberty Bell.

[Mike]

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.

[SHADOW HUNTER ALPHA]

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.

[taita cakes]

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

Point, please?

[The Infinite Shindig]

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