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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:

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.

Concept Concept Concept Concept Concept Concept Concept Concept Concept

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

Mixture Problems | Algebra – Problem 1: – Diagram Mixture Problems | Algebra – Problem 1: – Diagram Mixture Problems | Algebra – Problem 1: – Diagram

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Mixture Problems | Algebra – Problem 1: – Diagram Mixture Problems | Algebra – Problem 1: – Diagram Mixture Problems | Algebra – Problem 1: – Diagram Mixture Problems | Algebra – Problem 1: – Diagram

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

Mixture Problems | Algebra – Problem 2: – Diagram Mixture Problems | Algebra – Problem 2: – Diagram Mixture Problems | Algebra – Problem 2: – Diagram

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Mixture Problems | Algebra – Problem 2: – Diagram Mixture Problems | Algebra – Problem 2: – Diagram Mixture Problems | Algebra – Problem 2: – Diagram Mixture Problems | Algebra – Problem 2: – Diagram

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

Mixture Problems | Algebra – Problem 3: – Diagram Mixture Problems | Algebra – Problem 3: – Diagram Mixture Problems | Algebra – Problem 3: – Diagram

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Mixture Problems | Algebra – Problem 3: – Diagram Mixture Problems | Algebra – Problem 3: – Diagram Mixture Problems | Algebra – Problem 3: – Diagram Mixture Problems | Algebra – Problem 3: – Diagram

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

Mixture Problems | Algebra – Problem 4: – Diagram Mixture Problems | Algebra – Problem 4: – Diagram Mixture Problems | Algebra – Problem 4: – Diagram

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Mixture Problems | Algebra – Problem 4: – Diagram Mixture Problems | Algebra – Problem 4: – Diagram Mixture Problems | Algebra – Problem 4: – Diagram Mixture Problems | Algebra – Problem 4: – Diagram
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