Mixture Problems

Mixture problems involve combining two or more quantities with different concentrations or values to form a single mixture with a desired property (such as concentration, strength, or cost).

General Principle:

The total amount of a substance from all parts is equal to the amount of that substance in the resulting mixture.

$$ v_1c_1 + v_2c_2 = (v_1 + v_2)c_f $$

Where:

$v_1$, $v_2$ – volume or weight of each component
$c_1$, $c_2$ – concentration, strength, or unit value of each component
$c_f$ – final concentration or value of the resulting mixture

Alternate Form:

You may also express each part individually as:

$$ \text{Amount} = \text{Volume} \times \text{Concentration} $$

This principle applies whether you are working with salt in water, alcohol in liquid, or cost per kilogram in blended goods.

Problem 1:

The Jager-Bomb is a popular party-starting shot. Normally a 4.2-ounce mix contains 35% Jägermeister. Arataki Itto likes to act tough and wants to try a mix with 70% Jägermeister. How many ounces of pure Jägermeister must be added to a normal mix to obtain the desired mix? Ans. 4.9

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Problem 2:

Vessel A contains a mixture of 12 liters of wine and 18 liters of water. Vessel B contains 9 liters of wine and 3 liters of water. A certain amount must be drawn from vessel A and B to produce a mixture containing 7 liters of wine and 7 liters of water. How many liters must be drawn from Vessel A? Ans. 10 liters

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Problem 3:

A 100-kilogram salt solution is originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated? Ans. 20kg

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Problem 4:

A chemist has 300 grams of 20% acid solution. He wishes to drain some off and replace it with an 80% solution so as to obtain a 25% solution. How many grams must he drain and replace with 80% solution? Ans. 25 grams

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