How many mls of vodka should i add to 400ml of beer so that the resulting mixture contains 12% alcohol?

Question

Assuming that beer contains 5% alcohol while vodka contains 40%

https://math.stackexchange.com/questions/3783139/new-mix-of-drink-with-different-strong-alcohol — , Aug 08 '20 at 00:13
Does this answer your question? New mix of drink with different strong alcohol In the meantime, please show what you have tried to get an answer. — Toby Mak, Aug 08 '20 at 00:18
@TobyMak In the meanwhile I would suggest to take a bomb shot. — Michael Hoppe, Aug 08 '20 at 19:03

score 1 · Accepted Answer · answered Aug 08 '20 at 00:27

1

Let $x$ be the amount of vodka to add.

The amount of liquid in the mixture is $400+x$.

As the liquid is $12\%$ alcohol, so he amount of alcohol in the liquid is $0.12 (400 + x)$.

The beer is $5%$ alcohol so the amount of alcohol from the beer is $0.05\times 400$.

And the vodka is $40\%$ alcohol so the amount of alcohol from the vodka is $0.4\times x$.

So the total amount of alcohol in the liquid is $0.05 \times 400 + 0.4 x$.

And the total amount of alcohol in the liquid is $0.12(400+x)$.

So.......

answered Aug 08 '20 at 00:27

fleablood

Oh i almost got it right.Got it wrong about the amount of alcohol.Thanks fleablood. – William Aug 08 '20 at 00:30
That's not quite exact as there will occur a volume contraction if water and alcohol are mixed. For example, mixing 50 ml ethanol and 50 ml water will give a total volume of 96 ml. – Michael Hoppe Aug 08 '20 at 13:24
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Pfft.... real worlds only important to those who choose to live in it. – fleablood Aug 08 '20 at 15:38

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