Calculating ABV from blended batches

[TwistedGray]

I am sure I am way over thinking this and someone smarter than me will explain it in a few seconds.

I have:
5 gallons of beer at 7.5% ABV
1 gallon of beer at 7.0% ABV
8 ounces of whiskey at 40% ABV

How do I calculate what the combined ABV is?

 

[Vale71]

(a1Xv1)+(a2Xv2)+(a3Xv3)/(v1+v2+v3)

Where aX is the ABV (expressed in decimal notation) of liquid X and vX is the volume of liquid X.

 

[bob1852]

The ol' c1*v1=c2*v2

Comes to mind...

c = abv
v = volume

c1*v1 = 37.5 (7.5% *5 gal)
c2*v2 = 7 (7% * 1 gal)
c3*v3 = 2.5 (40% * 0.0625gal)

37.5+7+2.5=47

47 (total abv units) /6.0625 (total volume)=7.75

I get ~7.75%

 

[Silver_Is_Money]

V1*ABV1 + V2*ABV2 = (V1+V2)*X

Solve for X, wherein X = the blended ABV.

 

[TwistedGray]

I can understand the beer part, but I don't understand how to calculate the whiskey addition.

.0625 gallons = 8 ounces

40% x .0625 = 2.5
or
.4 x 0.0625 = 0.025

I don't know how you got 20 @AZ_IPA -- scratching my head.

 

[bob1852]

I can understand the beer part, but I don't understand how to calculate the whiskey addition.

.0625 gallons = 8 ounces

40% x .0625 = 2.5
or
.4 x 0.0625 = 0.025

I don't know how you got 20 @AZ_IPA -- scratching my head.

Sorry, it is 2.5...

The first time I did the calculation I inadvertently used 0.5 rather than 0.0625 (was thinking 8oz was a 0.5 of a gallon....i.e. 8oz being 0.5lb. Oops...)

The final answer (7.75%) is correct, I just didn't show my work right. At least I think it's correct. Lol.

 

[bleme]

I can understand the beer part, but I don't understand how to calculate the whiskey addition.

.0625 gallons = 8 ounces

40% x .0625 = 2.5
or
.4 x 0.0625 = 0.025

I don't know how you got 20 @AZ_IPA -- scratching my head.

Change his 20 to 2.5 and it all works - just a typo because the sum is right.

 

[Vale71]

It's time you silly 'mericans finally switched to the metric system...

 

[Silver_Is_Money]

It's time you silly 'mericans finally switched to the metric system...

If only it could happen, it would make life so much easier.

 

[TwistedGray]

Thanks again! Had me all sorts of confused for a moment.