Hello all, not sure if it's the right place to post this but anyway

I would like to know how to calculate a color that my display should show when combining the background and foreground colors..
Not sure how to describe, but say I have an foreground RGB value that is white, and a background RGB value that is black. I would like to add some transparency to the foreground color, so it should display a grey on the black background.
How to do this (for any foreground/background combination) ? There must be some algorithms but I don't find, or don't know what to search for.
An example, in Paint.NET I make a red background, and then I place a yellow pixel with an alpha value of 200. Then use the color picker tool to retrieve the color of the pixel I've just placed:
R G B A
Red: 255, 0, 0 255
Yellow: 220, 216, 0 200
Result: 227, 169, 0 255
I can't find the calculation required to obtain this RGB result.
Thanks for any help

Edit: I've found the answer!..
R = 227 = ( (200/255) * 220 ) + ( (1 - (200/255)) * 255 )
G = 169 = ( (200/255) * 216 ) + ( (1 - (200/255)) * 0 )
B = 0 = ( (200/255) * 0 ) + ( (1 - (200/255)) * 0 ) ...
