The furniture on the books of August 31 had an estimated salvage value of $4150 and 12 year life.
In August furniture - 37270 now in September 37780

I used the September one.
37780 - 4150/12 = 2802.5
Is this right?

there has been an increase in your furnituer account of R37780-R37270 from the month of August to September. "Depriciation is the cost of using an asset". So, we do not know whether we have used the new asset that we bought or not since we are not given the date of purchase, but how ever we can still use some assumption here. So let us assume that we did use the furniture. Then first you need to know that you should always separate the new acquired assets from the old ones when calculating depriciation to avoid confusion. Then we have: R37720-R4150=Answer/12=answer(p/a). However, I am not sure as to how much time we are calculating this depriciation for since it is not given on the information you have supplied. However by the look of things it seems like we have to calculate it for just one month. Then Answer(p/a)/12(months in a year)=depriciation for the old furniture. Then calculating depriciation for the new furniture: R37780-R37270=new furniture (cost), then New furniture cost/12(useful life)/12(months)=depriciation for new furniture. Then add depriciation for old furniture with the depriciation for the new furniture, that equals to the depriciation charge for the period.

Couple of comments here. First of all, just based on the information given, it should be completely irrelevant whether the furniture has been used. There is one depreciation method that is based on use, but would not be used for furniture. (And this is being done straight-line. I don't know if it's supposed to be straight-line because it doesn't say, but that's how it was done.) And there are some advanced concepts where an asset purchased might be treated differently, but it certainly would not apply to something on this level and there is no information leading anyone to believe that something like this would exist. I somewhat disagree with that definition of depreciation and you can't take that word "using" literally like that.

Second, there is not enough information on the new purchase to depreciate it. i.e. like whether there's a salvage value. If you're depreciating for August, do the August number only. If you had to depreciate for both months, you'd have to count the August number twice, once for August's depreciation and once for September's. And then the new purchase would only have one month's depreciation.

The information to make this decision has not been listed. No one can know whether you need to use August or September if you don't provide the information. i.e. you need to include what month you're doing depreciation for, what method is being used, etc. This information is too ambiguous to give a certain answer.