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%

Answer 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.......