How do I mathematically calculate the equation for the correct % of alcohol?

Question

Ive got two bottles of alcohol:

-One is 151 proof (75.5% alc)
-the other 80 proof (40% alc)

I want to mix the two and make a concoction of 120 proof or 60% alcohol. How do I equate this properly?

If it helps, lets say Ive got two one Litre bottles of each of those and only need to come up with one Litre of my new 120 proof alcohol.

Thanks everyone! < hiccup>

Thanks Stephen!

Actually... you lost me. Im stuck how you derive the 40/71 or how you get the .355 ? ? ?

Math as never my subject, but I can do animation and art.

Thanks for the help.

Your version sounds much more clear, but im again stuck at how you come up with ".355". I also dont see how the .2 just arrived in the equation.

It would be nice to figure this out with your help. Im trying to create 68% alcohol mix from 40% vodka and 75.5% Everclear.

Your help would be so much appreciated! -Dave

Answer 1

You expect to end up with 1L of 120 proof hootch. Therefor you have an ending percentage of 60% alcohol and 40% water.
So the volume of alcohol is .6 L and water is .4 L.
Let X be the quantity of Bacardi 151 and Y be the quantity of cheap rum.
You are then working to figure out X liters * (.755 Alcohol ) and Y liters * (.4 alcohol ) = .6 L alcohol
In algebra-speak, that is X (.755) + Y(.4) = .6
You also know that X + Y = 1 liter. Taking this equation and solving for Y we have Y = 1 - X.
We can now substitute all occurances of Y in the equation with (1-X) Therefor
X (.755) + (1-X)(.4) = .6 and we have a single variable to solve for.
.755X + .4 - .4X = .6 liters
.355X = .2 liters
X = .2/.355
X = .56338 liters of Bacardi 151
There for Y = .43662 liters of cheap rum.
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Additional info.
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OK, Shirt Sorry you got lost. But I skipped a step.
In my solution, this is what happened between
.755X + .4 - .4X = .6 liters and .355X = .2 liters

.755X + .4 - .4X = .6
Subtract .4 from both sides
.755X - .4X = .2
Subtract .4X from .755X
.355X = .2

I like steph's solution too.
He doesnt show all the steps either when solving for A.
(0.755A + 0.4(1-A))/1 = 0.6.
Get rid of the parenthesis by multiplying .4
(0.755A + 0.4 - 0.4A)/1 = 0.6.
Division by 1 doesn't change anything, So you can ditch the parenthesis.
0.755A + 0.4 - 0.4A = 0.6.
Subtract 0.4A from 0.755A
.355A + 0.4 = 0.6
.355A = 0.2

I assumed you were using rum because Bacardi is the only one that make a 151 proof liquor. Everclear is 190 or 95%. That will change your quantities alot. Use the same equation, but replace the 0.755 with 0.90.
I made my own version of Goldshlagers which is more than 100 proof. As you are doing, I too used Everclear to raise the proof. It ended up tasting better than the goldshlagers. Disolve a dozen Atomic Fireballs into a liter of vodka and add everclear.

Answer 2

I hope this is a theoretical question only ;)

If you mix a litres of the first bottle, and b litres of the second bottle, the total amount of alcohol will be 0.755a + 0.4b, so the percentage will be (0.755a+0.4b)/(a+b).

Thus, if we're assuming a and b add to 1, we want (0.755a + 0.4(1-a))/1 = 0.6.
So 0.355a + 0.4 = 0.6, so 0.355a = 0.2, so a = 40/71, or 0.56338 litres of the first bottle, mixed with 0.43662 litres of the second.

Answer 3

You would have a smart person do it cuz they smarted and u equal it by using math.
If u do that u can get a hear a take cuz that's 2 much achool and it would be like 121%