What quantity of water should be added to 3 liters of 10% salt solution so that it becomes 5% salt solution?

We want to find how much $q$ (in $\ell$) of solution $A$ with $25\%$ salt we must add with $3\ell$ of solution $B$ with $10\%$ salt to give a solution $A+B$ (this has nothing to do with the usual addition; it's just notation!) that has $15\%$ salt.

The invariant here is the saline content.

Thus, per litre, $A$ has $0.25q$ of salt, $B$ has $0.1×3$ of salt, and $A+B$ has $0.15(q+3)$ salt. Since the saline content is conserved, we must have that $$0.25q+0.3=0.15(q+3)$$ is true. This gives us $(0.25-0.15)q=0.45-0.3=0.15,$ or $$q=\frac{0.15}{0.10}=1.5.$$

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