# A pharmacist needs to obtain a 70% alcohol solution. How many ounces of a 30% solution must be mixed with 40 ounces of an solution to obtain a 70% solution?

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A mother solution or a pure solvent can be diluted down to give a lower solution; but you can't dilute down to give a higher concentration, i.e. to go from 30% to 70%. We don't know whether it is v/v% or m/m% .

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To obtain a 70% alcohol solution, the pharmacist needs to mix 20 ounces of the 30% solution with 40 ounces of the solution.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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