You wouldn't really have to do math to accomplish this, if you want to try some other time. I did okay in math as a kid (eons ago!), but these days I will go to some lengths to avoid it if possible. Graph paper is good, but if you want to visualize it, tape some newspaper together and cut the exact size of your finished back. Then draw around the edges the width that you want for your border. Measure the inner part and add a half inch in length and width for seams. Then be sure to also add a quarter inch seam allowance to the border. On the other hand, you might want to make the border parts generous for trimming, as you would for any other backing.
The bigger challenge would be centering this pieced backing so that it's even all around because I'm assuming your batting will be sticking out a few inches on all sides.
I agree with Kelsie - you need to be kinder to yourself! Most of the time my backs are as plain as possible because I don't want to create extra opportunities to make errors. I make plenty of boo boos on the top! I think your decision to just make a plain back is perfectly okay!