Calculating ABV from blended worts

So I’ve finally kegged up my old ale.  I overshot the OG (1.12 instead of 1.095).

After it fermented down to 1.044, I split the batch into two separate carboys and added more wort.  The batch I added was a total of 3 gallons (1.5 gallons when to each of the 2.5 of the previous batch) brewed with 4 lbs. DME.

This mix fermented down to about 1.02 (I don’t have my notes handy).

So, if I wanted to figure out the final ABV, would I take a weighted average of the two starting gravities and use that to compute with the final final gravity?

If I take a weighted average of the starting gravities, I come out at 1.096, which is right where I wanted to be.  Blind luck, since I didn’t calculate this before…

Just curious if anyone has thoughts on the right way to calculate this, since everyone asks how strong it is.

FWIW, it’s a damn fine beer.  One batch has been on tap, the other is aging and I think I might bottle it.

Weighted average - I don’t think there is any other way.

You could just pick a number and tell it to them authoritatively.  That would probably be the easiest answer.

I think the easiest way to get an accurate answer is to just keep track of the total wort volume and the total fermentables in the batch.  If you had the OG and volume of the original batch, figure out the total points present (sounds like 120 * 5 = 600). So you added 3 gallons containing 4 lbs DME.  DME is about 45 points/pound, so you added 180 points.  So you have 600 + 180 = 780 points in 5 + 3 = 8 gallons.  Your adjusted OG is 780/8 = 1.098.

If you fermented that down to 1.020, then your ABV is (1.098 - 1.020) * 131.25 = 10.2%

Gordon - You’re correct.  1.02 (edited above).

Glad to see my approach was correct.  If not my typing…

Minor detail check: the OG was 1.120, not 1.112. So the weighted OG is ~1.098, and the ABV is ~10.2%.

Thanks. Misread it the first time. Fixed in my post.