HELP: ABV dilution calculating!!!

[WineAllDay]

Riddle me this community:

1) If I filled up a 10 gallon cooler with orange juice and 2 liters bottles of vodka with 40% abv each; then divided the batch in bottles of 12oz. How much ABV is in each 12oz bottle?

2) Also if I filled up another 10 gallon cooler with orange juice and added 2 750ml bottles of vodka with 40% abv each; then divided the batch in bottles of 12oz, how much ABV is in each 12oz bottle?

 

[Beernik]

1) ≈ 2% ABV. It doesn’t matter how many you divide it into, assuming it is completely mixed.

2) ≈ 1.5% ABV, because it’s 1/2 a liter less vodka.

(Rule of thumb, 1 L is a little larger than 1/4 gallon)

 

[BrewnWKopperKat]

Riddle me this community

I'll offer a "2nd set of eyes" for what @Beernik suggested:

eta: does someone have a good article on how to calculate dilution?

 

[Beernik]

Weighted volume average:

(V1*A1 + V2*A2) / (V1 + V2) = A_mixed

Also, 3.8 proof = 1.9% ABV, & I said, ≈ 2%.

It’s also ≈ 0.528 gallons

 

[WineAllDay]

Thanks so much to all and following up on this. If I poured 4 liters of vodka in a 5 gallon cooler with the same orange juice or water, would the ABV be 8%?

 

[WineAllDay]

What would be the percentage with the same 4 liters of vodka and let's say 3 gallons or orange juice/water?

 

[WineAllDay]

@BrewnWKopperKat , so would the answer be correct or a miscalculation?

 

[BrewnWKopperKat]

@WineAllDay, #2 answered the 1st question. #4 provides the equations to answer the other questions. I don't have time to be a "second set of eyes" (#3) this time around.