So I know this question is now almost a year old, but I had the same problem and found the solution so I thought I'd share it. The term for this is "alpha compositing" and wikipedia has a great article on it.
http://en.wikipedia.org/wiki/Alpha_compositing
In your case you are compositing your color with a fully opaque white rgba(255,255,255,1).
I made an excel calculator to do this. I couldn't figure out how to put the cell values themselves into StackOverflow, so here's a screenshot of the forumulas. Orange cells are for your input.
You can then change A10-A13 to define your initial color and D10 to specify your desired alpha.
Combined known colors
Color 1 Color 2 Combined
A 0.15 1 =$B$3+$C$3*(1-$B$3)
R 255 255 =(1/($D$3))*(B4*$B$3+C4*$C$3*(1-$B$3))
G 0 255 =(1/($D$3))*(B5*$B$3+C5*$C$3*(1-$B$3))
B 0 255 =(1/($D$3))*(B6*$B$3+C6*$C$3*(1-$B$3))
1 Known Color, Known result Alpha
Color 1 Color 2 Combined
A 0.15 =(D10-B10)/(1-B10) 0.85
R 255 255 =(1/($D$10))*(B11*$B$10+C11*$C$10*(1-$B$10))
G 255 255 =(1/($D$10))*(B12*$B$10+C12*$C$10*(1-$B$10))
B 0 255 =(1/($D$10))*(B13*$B$10+C13*$C$10*(1-$B$10))