Solving an Algebraic Headache: Proving Kt+1 = 1.15 * K

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The discussion revolves around proving the equation Kt+1 = 1.15 * Kt, correcting an initial misunderstanding of the notation. Participants clarify that the original problem likely contains a typo, suggesting the intended equation should relate Kt+1 to Kt rather than an undefined K. They emphasize the importance of substituting known values and rearranging equations to simplify the proof. The conversation highlights the need to express Lt in terms of Kt and Yt to derive the desired relationship. Overall, the collaborative effort aims to resolve the algebraic confusion effectively.
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I have an algebra problem which is giving me headaches.

Lt = St
Lt = Kt+1 - Kt
St = s * Yt
Kt = k * Yt

K0 = 200, s = 0.3, k = 2

Prove that Kt+1 = 1.15 * K

Thanks.
 
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Flummoxed said:
I have an algebra problem which is giving me headaches.
Lt = St
Lt = Kt+1 - Kt
St = s * Yt
Kt = k * Yt
K0 = 200, s = 0.3, k = 2
Prove that Kt+1 = 1.15 * K
Thanks.

Now I'm not sure if this is correct, but I started off by subsituting in the known values.

Lt = St
Lt = Kt+1 - Kt
St = 0.3 * Yt
Kt = 2 * Yt

-----------------

Lt = St
Lt = Kt+1 - Kt
St = 0.3 * (0.5 * Kt)
0.5 * Kt = Yt
 
Flummoxed said:
I have an algebra problem which is giving me headaches.
Lt = St
Lt = Kt+1 - Kt
St = s * Yt
Kt = k * Yt
K0 = 200, s = 0.3, k = 2
Prove that Kt+1 = 1.15 * K
Thanks.

Since the very first equations says Lt= St, you can simplify slightly by writing that third equation as Lt= 0.3Yt. You now have 3 equations:
Lt= Kt+1- Kt
Lt= s Yt
Kt= k Yt

Also, You say you want to prove "Kt+1= 1.15*K" which makes no sense. I imagine it must be either "Kt+1= 1.15*k" or "Kt+1= 1.15*Kt". I suspect it is the latter.

Since, however, you want Kt+1= something, I suggest rewriting that first equation as Kt+1= Lt + Kt (add Kt to both sides). Now, it looks to me like you just need to replace that Lt with something!

You know that Lt= sYt. do you see that Yt= (1/k) Kt? That should make it clear!
 
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The sheet I was given says "Prove that Kt+1 = 1.15 x K" with the K in upper case.
 
Flummoxed said:
The sheet I was given says "Prove that Kt+1 = 1.15 x K" with the K in upper case.
I think that's a little typo. The sheet should read:
Kt + 1 = 1.15 Kt.
---------------
You can follow HallsofIvy's post, and you'll soon arrive at the answer,
or you may also want to try a slightly different way:
St = Lt
<=> s Yt = Kt + 1 - Kt.
What's Kt + 1? What's Kt?
Can you go from here?
 
I have also been able to confirm that the equation:

Kt+1 = 1.15 * K

should read:

Kt+1 = 1.15 * Kt

From the help that HallsofIvy and VietDao29 provided, you should come to the answer.

I came to the answer a different way, but want to find out if you can use their help before I make another post.
 
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