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# How do I calculate which concentration of Vinegar is cheapest, before diluting it? [closed]

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Closed as off topic by Mithrandir24601‭ on Sep 12, 2023 at 23:25

This question is not within the scope of Physics.

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Presuppose that I need vinegar of $c$ concentration, where $c$ < any concentration listed below. Let $w$ be the price of water that I'll use to dilute.

How do I deduce which concentration (of Vinegar) is cheapest to buy? I shall dilute it to c concentration.

Solace Labs' concentrations Price / 100 mL, for 946 mL jug
25% $6.33 45%$7.54
75% $10.57 Calyptus' concentrations Price / 100 mL 30%$2.12
45% $2.52 75%$6.92
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Let w be the price of water that I'll use to dilute.

Forget that. Unless you are in extraordinary circumstances, the price of water is so low compared to the vinegar as to be irrelevant.

How do I deduce which concentration (of Vinegar) is cheapest to buy?

Consider the price of only the vinegar portion of each solution you can buy. For example, if 500 ml of 45% solution costs \$3.00, then the price of just the vinegar part is \$3.00/45% = $6.67 per 500 ml. Do this for each of the possibilities, and normalize them all to the same volume. Let's say you normalize all to the cost of 100 ml of actual vinegar. In the example above, the price would \$1.33 per 100 ml. Repeat for each offering and compare.

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