# Algebra problem

1. Jan 18, 2006

### Flummoxed

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.

2. Jan 18, 2006

### Flummoxed

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

3. Jan 18, 2006

### HallsofIvy

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!

Last edited by a moderator: Jan 18, 2006
4. Jan 18, 2006

### Flummoxed

The sheet I was given says "Prove that Kt+1 = 1.15 x K" with the K in upper case.

5. Jan 18, 2006

### VietDao29

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?

6. Jan 18, 2006

### matrixx333

I have also been able to confirm that the equation:

Kt+1 = 1.15 * K