Water & salt liquid

Question

If I'd have an $500$ ml bottle of water and it would have $1\%$ salt, how much I would need to add water to make it, lets say $0.3\%$? I cannot find the way to figure this problem. Could anyone provide the formula to solve this? Regards, TuukkaX.

Answer 1

You may think in the following way.

In $100$ ml of water, there is $1$ gr of salt (this is what $1\%$ means).

In $500$ ml of water, there are $5$ gr of salt.

Now, you want to add some water in order to obtain that specific percentage. The quantity of salt remains just the same. Let's say that we add $x$ ml of water. What we have is the following:

In $(500+x)$ ml of water, there are $5$ gr of salt.

In $100$ ml of water there are $0.3$ gr of salt (this is what we want).

Now, I think it is easy to find the unknown $x$.

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Consider that these two variables are proportional. Thus, we have to solve the equation: $$\frac{500+x}{100} = \frac{5}{0.3}.$$ Now, it must be easy to solve for $x$.