Proof Spirit Calculations

Question

The amount of 190 proof required to make 500 ml of 70% alcohol is?

The answer is 368 ml. Just couldn't figure how to get to that answer. Help me out, aye?

Answer 1

$500$ ml of 70% alcohol has $0.7 \times 500 = 350$ ml of alcohol in it. $190$ proof hooch is $95$% alcohol. If $x$ is the number of ml needed, then $95$% of $x$ had better be $350$. That is $0.95 x = 350$, so $x= 350/0.95 = 368.42...$

Answer 2

So apparently we are mixing a strong alcohol ($190/2 = 95\%$) and water ($0\%$ alcohol) and we want a total of $0.5$ l of this mixture, and we want it to contain $70~\%$ alcohol. Let's assume that these are volume percentages. May the amount of alcohol be $A$. Then the amount of alcohol in the final product is $0.95A$, which should, on the other hand, be equal to $0.7 \times 0.5$. Therefore, $A=\frac{0.7 \times 0.5}{0.95}\approx 0.3684$.